메뉴 건너뛰기




Volumn 471, Issue 3-4, 2009, Pages 113-219

Black holes, qubits and octonions

Author keywords

Black hole; Entanglement; Hyperdeterminant; Octonion; Qubit

Indexed keywords


EID: 61549136749     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physrep.2008.11.002     Document Type: Review
Times cited : (121)

References (243)
  • 1
    • 33750485765 scopus 로고
    • Black holes and entropy
    • Bekenstein J.D. Black holes and entropy. Phys. Rev. D7 (1973) 2333-2346
    • (1973) Phys. Rev. , vol.D7 , pp. 2333-2346
    • Bekenstein, J.D.1
  • 2
    • 84938421990 scopus 로고
    • Particle creation by black holes
    • Hawking S.W. Particle creation by black holes. Comm. Math. Phys. 43 (1975) 199-220
    • (1975) Comm. Math. Phys. , vol.43 , pp. 199-220
    • Hawking, S.W.1
  • 3
    • 34447647125 scopus 로고    scopus 로고
    • String triality, black hole entropy and Cayley's hyperdeterminant
    • arXiv:hep-th/0601134
    • Duff M.J. String triality, black hole entropy and Cayley's hyperdeterminant. Phys. Rev. D76 (2007) 025017. arXiv:hep-th/0601134
    • (2007) Phys. Rev. , vol.D76 , pp. 025017
    • Duff, M.J.1
  • 4
    • 33646860959 scopus 로고    scopus 로고
    • Strings, black holes, and quantum information
    • arXiv:hep-th/0602061
    • Kallosh R., and Linde A. Strings, black holes, and quantum information. Phys. Rev. D73 (2006) 104033. arXiv:hep-th/0602061
    • (2006) Phys. Rev. , vol.D73 , pp. 104033
    • Kallosh, R.1    Linde, A.2
  • 5
    • 33746547779 scopus 로고    scopus 로고
    • Stringy black holes and the geometry of entanglement
    • arXiv:hep-th/0603136
    • Levay P. Stringy black holes and the geometry of entanglement. Phys. Rev. D74 (2006) 024030. arXiv:hep-th/0603136
    • (2006) Phys. Rev. , vol.D74 , pp. 024030
    • Levay, P.1
  • 6
    • 34447640199 scopus 로고    scopus 로고
    • 7 and the tripartite entanglement of seven qubits
    • arXiv:quant-ph/0609227
    • 7 and the tripartite entanglement of seven qubits. Phys. Rev. D76 (2007) 025018. arXiv:quant-ph/0609227
    • (2007) Phys. Rev. , vol.D76 , pp. 025018
    • Duff, M.J.1    Ferrara, S.2
  • 7
    • 33846416900 scopus 로고    scopus 로고
    • Strings, black holes, the tripartite entanglement of seven qubits and the Fano plane
    • arXiv:hep-th/0610314
    • Levay P. Strings, black holes, the tripartite entanglement of seven qubits and the Fano plane. Phys. Rev. D75 (2007) 024024. arXiv:hep-th/0610314
    • (2007) Phys. Rev. , vol.D75 , pp. 024024
    • Levay, P.1
  • 8
    • 37349042147 scopus 로고    scopus 로고
    • 6 and the bipartite entanglement of three qutrits
    • arXiv:0704.0507 [hep-th]
    • 6 and the bipartite entanglement of three qutrits. Phys. Rev. D76 (2007) 124023 arXiv:0704.0507 [hep-th]
    • (2007) Phys. Rev. , vol.D76 , pp. 124023
    • Duff, M.J.1    Ferrara, S.2
  • 9
    • 36348935461 scopus 로고    scopus 로고
    • A three-qubit interpretation of BPS and non-BPS STU black holes
    • arXiv:0708.2799 [hep-th]
    • Levay P. A three-qubit interpretation of BPS and non-BPS STU black holes. Phys. Rev. D76 (2007) 106011 arXiv:0708.2799 [hep-th]
    • (2007) Phys. Rev. , vol.D76 , pp. 106011
    • Levay, P.1
  • 10
    • 35348998065 scopus 로고    scopus 로고
    • Attractors with vanishing central charge
    • arXiv:0707.2730 [hep-th]
    • Bellucci S., Marrani A., Orazi E., and Shcherbakov A. Attractors with vanishing central charge. Phys. Lett. B655 (2007) 185-195 arXiv:0707.2730 [hep-th]
    • (2007) Phys. Lett. , vol.B655 , pp. 185-195
    • Bellucci, S.1    Marrani, A.2    Orazi, E.3    Shcherbakov, A.4
  • 12
    • 61549113282 scopus 로고    scopus 로고
    • S. Ferrara, K. Hayakawa, A. Marrani, Erice lectures on black holes and attractors. arXiv:0805.2498 [hep-th]
    • S. Ferrara, K. Hayakawa, A. Marrani, Erice lectures on black holes and attractors. arXiv:0805.2498 [hep-th]
  • 13
    • 55549144366 scopus 로고    scopus 로고
    • 7 (7) invariant measures of entanglement
    • 7 (7) invariant measures of entanglement. Fortschr. Phys. 56 7-9 (2008) 842-848
    • (2008) Fortschr. Phys. , vol.56 , Issue.7-9 , pp. 842-848
    • Borsten, L.1
  • 14
    • 61549101359 scopus 로고    scopus 로고
    • P. Levay, P. Vrana, Three fermions with six single particle states can be entangled in two inequivalent ways. arXiv:0806.4076 [quant-ph]
    • P. Levay, P. Vrana, Three fermions with six single particle states can be entangled in two inequivalent ways. arXiv:0806.4076 [quant-ph]
  • 15
    • 61549101049 scopus 로고    scopus 로고
    • S. Bellucci, S. Ferrara, A. Marrani, A. Yeranyan, STU black holes unveiled. arXiv:0807.3503 [hep-th]
    • S. Bellucci, S. Ferrara, A. Marrani, A. Yeranyan, STU black holes unveiled. arXiv:0807.3503 [hep-th]
  • 16
    • 61549121209 scopus 로고    scopus 로고
    • P. Levay, M. Saniga, P. Vrana, Three-Qubit operators, the split Cayley hexagon of order two and black holes. arXiv:0808.3849 [quant-ph]
    • P. Levay, M. Saniga, P. Vrana, Three-Qubit operators, the split Cayley hexagon of order two and black holes. arXiv:0808.3849 [quant-ph]
  • 17
    • 61549086668 scopus 로고    scopus 로고
    • L. Borsten, D. Dahanayake, M.J. Duff, H. Ebrahim, W. Rubens, Freudenthal triple classification of three-qubit entanglement. arXiv:0812.3322 [quant-th]
    • L. Borsten, D. Dahanayake, M.J. Duff, H. Ebrahim, W. Rubens, Freudenthal triple classification of three-qubit entanglement. arXiv:0812.3322 [quant-th]
  • 18
    • 0346688149 scopus 로고    scopus 로고
    • Distributed entanglement
    • arXiv:quant-ph/9907047
    • Coffman V., Kundu J., and Wootters W.K. Distributed entanglement. Phys. Rev. A61 (2000) 052306. arXiv:quant-ph/9907047
    • (2000) Phys. Rev. , vol.A61 , pp. 052306
    • Coffman, V.1    Kundu, J.2    Wootters, W.K.3
  • 19
    • 0030584033 scopus 로고    scopus 로고
    • Four-dimensional string-string-string triality
    • arXiv:hep-th/9508094
    • Duff M.J., Liu J.T., and Rahmfeld J. Four-dimensional string-string-string triality. Nuclear Phys. B459 (1996) 125-159. arXiv:hep-th/9508094
    • (1996) Nuclear Phys. , vol.B459 , pp. 125-159
    • Duff, M.J.1    Liu, J.T.2    Rahmfeld, J.3
  • 21
    • 0347269195 scopus 로고    scopus 로고
    • Multipartite entanglement and hyperdeterminants
    • arXiv:quant-ph/0212146
    • Miyake A., and Wadati M. Multipartite entanglement and hyperdeterminants. Quantum. Inf. Compt. 2 (Special) (2002) 540-555. arXiv:quant-ph/0212146
    • (2002) Quantum. Inf. Compt. , vol.2 Special , pp. 540-555
    • Miyake, A.1    Wadati, M.2
  • 22
    • 0002093582 scopus 로고
    • On the theory of linear transformations
    • Cayley A. On the theory of linear transformations. Camb. Math. J. 4 (1845) 193-209
    • (1845) Camb. Math. J. , vol.4 , pp. 193-209
    • Cayley, A.1
  • 23
    • 52649115555 scopus 로고    scopus 로고
    • MAA online
    • E. Pegg Jr., The fano plane, MAA online. http://www.maa.org/editorial/mathgames/mathgames_05_30_06.html
    • The fano plane
    • Pegg Jr., E.1
  • 26
    • 52649101530 scopus 로고    scopus 로고
    • Black hole entropy and quantum information
    • arXiv:hep-th/0612036
    • Duff M.J., and Ferrara S. Black hole entropy and quantum information. Lecture Notes in Phys. 755 (2008) 93-114. arXiv:hep-th/0612036
    • (2008) Lecture Notes in Phys. , vol.755 , pp. 93-114
    • Duff, M.J.1    Ferrara, S.2
  • 28
    • 61549138546 scopus 로고    scopus 로고
    • L. Manivel, Configurations of lines and models of Lie algebras. arXiv:math/0507118
    • L. Manivel, Configurations of lines and models of Lie algebras. arXiv:math/0507118
  • 29
    • 61549143492 scopus 로고    scopus 로고
    • Alberto Elduque, The magic square and symmetric compositions II. arXiv:math/0507282
    • Alberto Elduque, The magic square and symmetric compositions II. arXiv:math/0507282
  • 30
    • 0001619610 scopus 로고    scopus 로고
    • Orbits of exceptional groups, duality and BPS states in string theory
    • arXiv:hep-th/9708025
    • Ferrara S., and Gunaydin M. Orbits of exceptional groups, duality and BPS states in string theory. Internat. J. Modern Phys. A13 (1998) 2075-2088. arXiv:hep-th/9708025
    • (1998) Internat. J. Modern Phys. , vol.A13 , pp. 2075-2088
    • Ferrara, S.1    Gunaydin, M.2
  • 31
    • 33750610508 scopus 로고    scopus 로고
    • Lectures on on black holes, topological strings and quantum attractors
    • arXiv:hep-th/0607227
    • Pioline B. Lectures on on black holes, topological strings and quantum attractors. Classical Quantum Gravity 23 (2006) S981. arXiv:hep-th/0607227
    • (2006) Classical Quantum Gravity , vol.23
    • Pioline, B.1
  • 32
    • 0003883002 scopus 로고    scopus 로고
    • P-brane democracy
    • arXiv:hep-th/9507048
    • P.K. Townsend, P-brane democracy. arXiv:hep-th/9507048
    • Townsend, P.K.1
  • 33
    • 0030580754 scopus 로고    scopus 로고
    • Heterotic and type I string dynamics from eleven dimensions
    • arXiv:hep-th/9510209
    • Horava P., and Witten E. Heterotic and type I string dynamics from eleven dimensions. Nuclear Phys. B460 (1996) 506-524. arXiv:hep-th/9510209
    • (1996) Nuclear Phys. , vol.B460 , pp. 506-524
    • Horava, P.1    Witten, E.2
  • 34
    • 0030600809 scopus 로고    scopus 로고
    • Five-branes and M-theory on an orbifold
    • arXiv:hep-th/9512219
    • Witten E. Five-branes and M-theory on an orbifold. Nuclear Phys. B463 (1996) 383-397. arXiv:hep-th/9512219
    • (1996) Nuclear Phys. , vol.B463 , pp. 383-397
    • Witten, E.1
  • 35
    • 0001220124 scopus 로고    scopus 로고
    • M theory (the theory formerly known as strings)
    • arXiv:hep-th/9608117
    • Duff M.J. M theory (the theory formerly known as strings). Internat. J. Modern Phys. A11 (1996) 5623-5642. arXiv:hep-th/9608117
    • (1996) Internat. J. Modern Phys. , vol.A11 , pp. 5623-5642
    • Duff, M.J.1
  • 36
    • 0004229359 scopus 로고
    • Salam A., and Sezgin E. (Eds), North-Holland, Amsterdam, Netherlands p. 1499. World Scientific, Singapore, Singapore, 1989, p. 1499
    • In: Salam A., and Sezgin E. (Eds). Supergravities in Diverse Dimensions. Vol. 1, 2 (1989), North-Holland, Amsterdam, Netherlands p. 1499. World Scientific, Singapore, Singapore, 1989, p. 1499
    • (1989) Supergravities in Diverse Dimensions. Vol. 1, 2
  • 37
    • 0042863571 scopus 로고    scopus 로고
    • Supergravity
    • arXiv:hep-th/0212245
    • B. de Wit, Supergravity. arXiv:hep-th/0212245
    • de Wit, B.1
  • 38
    • 0004335533 scopus 로고    scopus 로고
    • Introduction to supergravities in diverse dimensions
    • arXiv:hep-th/9802138
    • Y. Tanii, Introduction to supergravities in diverse dimensions. arXiv:hep-th/9802138
    • Tanii, Y.1
  • 39
    • 0001333921 scopus 로고
    • Supergravity theory in 11 dimensions
    • Cremmer E., Julia B., and Scherk J. Supergravity theory in 11 dimensions. Phys. Lett. B76 (1978) 409-412
    • (1978) Phys. Lett. , vol.B76 , pp. 409-412
    • Cremmer, E.1    Julia, B.2    Scherk, J.3
  • 40
    • 45949125881 scopus 로고
    • Superstrings in D = 10 from supermembranes in D = 11
    • Duff M.J., Howe P.S., Inami T., and Stelle K.S. Superstrings in D = 10 from supermembranes in D = 11. Phys. Lett. B191 (1987) 70
    • (1987) Phys. Lett. , vol.B191 , pp. 70
    • Duff, M.J.1    Howe, P.S.2    Inami, T.3    Stelle, K.S.4
  • 41
    • 0346926343 scopus 로고
    • String theory dynamics in various dimensions
    • arXiv:hep-th/9503124
    • Witten E. String theory dynamics in various dimensions. Nuclear Phys. B443 (1995) 85-126. arXiv:hep-th/9503124
    • (1995) Nuclear Phys. , vol.B443 , pp. 85-126
    • Witten, E.1
  • 42
    • 8644257680 scopus 로고
    • Dirichlet-Branes and Ramond-Ramond charges
    • arXiv:hep-th/9510017
    • Polchinski J. Dirichlet-Branes and Ramond-Ramond charges. Phys. Rev. Lett. 75 (1995) 4724-4727. arXiv:hep-th/9510017
    • (1995) Phys. Rev. Lett. , vol.75 , pp. 4724-4727
    • Polchinski, J.1
  • 43
    • 0041686993 scopus 로고    scopus 로고
    • Microscopic origin of the Bekenstein-Hawking entropy
    • arXiv:hep-th/9601029
    • Strominger A., and Vafa C. Microscopic origin of the Bekenstein-Hawking entropy. Phys. Lett. B379 (1996) 99-104. arXiv:hep-th/9601029
    • (1996) Phys. Lett. , vol.B379 , pp. 99-104
    • Strominger, A.1    Vafa, C.2
  • 46
    • 0011658957 scopus 로고
    • Target space duality in string theory
    • arXiv:hep-th/9401139
    • Giveon A., Porrati M., and Rabinovici E. Target space duality in string theory. Phys. Rep. 244 (1994) 77-202. arXiv:hep-th/9401139
    • (1994) Phys. Rep. , vol.244 , pp. 77-202
    • Giveon, A.1    Porrati, M.2    Rabinovici, E.3
  • 47
    • 0003152215 scopus 로고
    • Strong-weak coupling duality and nonperturbative effects in string theory
    • Font A., Ibanez L.E., Lust D., and Quevedo F. Strong-weak coupling duality and nonperturbative effects in string theory. Phys. Lett. B249 (1990) 35-43
    • (1990) Phys. Lett. , vol.B249 , pp. 35-43
    • Font, A.1    Ibanez, L.E.2    Lust, D.3    Quevedo, F.4
  • 48
    • 25344468080 scopus 로고
    • The confining phase of superstrings and axionic strings
    • Rey S.-J. The confining phase of superstrings and axionic strings. Phys. Rev. D43 (1991) 526-538
    • (1991) Phys. Rev. , vol.D43 , pp. 526-538
    • Rey, S.-J.1
  • 49
    • 0001495010 scopus 로고
    • Duality symmetries of 4-D heterotic strings
    • arXiv:hep-th/9305185
    • Schwarz J.H., and Sen A. Duality symmetries of 4-D heterotic strings. Phys. Lett. B312 (1993) 105-114. arXiv:hep-th/9305185
    • (1993) Phys. Lett. , vol.B312 , pp. 105-114
    • Schwarz, J.H.1    Sen, A.2
  • 50
    • 0001963140 scopus 로고
    • Four-dimensional string / string duality
    • arXiv:hep-th/9305142
    • Duff M.J., and Khuri R.R. Four-dimensional string / string duality. Nuclear Phys. B411 (1994) 473-486. arXiv:hep-th/9305142
    • (1994) Nuclear Phys. , vol.B411 , pp. 473-486
    • Duff, M.J.1    Khuri, R.R.2
  • 51
    • 13344278667 scopus 로고
    • Duality symmetric actions
    • arXiv:hep-th/9304154
    • Schwarz J.H., and Sen A. Duality symmetric actions. Nuclear Phys. B411 (1994) 35-63. arXiv:hep-th/9304154
    • (1994) Nuclear Phys. , vol.B411 , pp. 35-63
    • Schwarz, J.H.1    Sen, A.2
  • 52
    • 0002528930 scopus 로고
    • Quantization of dyon charge and electric magnetic duality in string theory
    • arXiv:hep-th/9209016
    • Sen A. Quantization of dyon charge and electric magnetic duality in string theory. Phys. Lett. B303 (1993) 22-26. arXiv:hep-th/9209016
    • (1993) Phys. Lett. , vol.B303 , pp. 22-26
    • Sen, A.1
  • 53
    • 0000066381 scopus 로고
    • Electric magnetic duality in string theory
    • arXiv:hep-th/9207053
    • Sen A. Electric magnetic duality in string theory. Nuclear Phys. B404 (1993) 109-126. arXiv:hep-th/9207053
    • (1993) Nuclear Phys. , vol.B404 , pp. 109-126
    • Sen, A.1
  • 54
    • 49449124108 scopus 로고
    • Magnetic monopoles as gauge particles?
    • Montonen C., and Olive D.I. Magnetic monopoles as gauge particles?. Phys. Lett. B72 (1977) 117
    • (1977) Phys. Lett. , vol.B72 , pp. 117
    • Montonen, C.1    Olive, D.I.2
  • 55
    • 4243643643 scopus 로고
    • Unity of superstring dualities
    • arXiv:hep-th/9410167
    • Hull C.M., and Townsend P.K. Unity of superstring dualities. Nuclear Phys. B438 (1995) 109-137. arXiv:hep-th/9410167
    • (1995) Nuclear Phys. , vol.B438 , pp. 109-137
    • Hull, C.M.1    Townsend, P.K.2
  • 56
    • 0002946073 scopus 로고
    • Strong / weak coupling duality from the dual string
    • arXiv:hep-th/9501030
    • Duff M.J. Strong / weak coupling duality from the dual string. Nuclear Phys. B442 (1995) 47-63. arXiv:hep-th/9501030
    • (1995) Nuclear Phys. , vol.B442 , pp. 47-63
    • Duff, M.J.1
  • 57
    • 0030597742 scopus 로고    scopus 로고
    • Evidence for heterotic/heterotic duality
    • arXiv:hep-th/9601036
    • Duff M.J., Minasian R., and Witten E. Evidence for heterotic/heterotic duality. Nuclear Phys. B465 (1996) 413-438. arXiv:hep-th/9601036
    • (1996) Nuclear Phys. , vol.B465 , pp. 413-438
    • Duff, M.J.1    Minasian, R.2    Witten, E.3
  • 58
    • 0001003385 scopus 로고
    • Classification of Kähler manifolds In N = 2 vector multiplet supergravity couplings
    • Cremmer E., and Van Proeyen A. Classification of Kähler manifolds In N = 2 vector multiplet supergravity couplings. Classical Quantum Gravity 2 4 (1985) 445-454
    • (1985) Classical Quantum Gravity , vol.2 , Issue.4 , pp. 445-454
    • Cremmer, E.1    Van Proeyen, A.2
  • 59
    • 0001988205 scopus 로고
    • Coupling of Yang-Mills to N = 4, D = 4 supergravity
    • Bergshoeff E., Koh I.G., and Sezgin E. Coupling of Yang-Mills to N = 4, D = 4 supergravity. Phys. Lett. B155 (1985) 71
    • (1985) Phys. Lett. , vol.B155 , pp. 71
    • Bergshoeff, E.1    Koh, I.G.2    Sezgin, E.3
  • 60
    • 0000444712 scopus 로고
    • Duality rotations in membrane theory
    • Duff M.J., and Lu J.X. Duality rotations in membrane theory. Nuclear Phys. B347 (1990) 394-419
    • (1990) Nuclear Phys. , vol.B347 , pp. 394-419
    • Duff, M.J.1    Lu, J.X.2
  • 62
    • 0042788474 scopus 로고
    • The S O (8) supergravity
    • Cremmer E., and Julia B. The S O (8) supergravity. Nuclear Phys. B159 (1979) 141
    • (1979) Nuclear Phys. , vol.B159 , pp. 141
    • Cremmer, E.1    Julia, B.2
  • 63
    • 34547655774 scopus 로고    scopus 로고
    • 11 origin of all maximal supergravities
    • arXiv:0705.0752 [hep-th]
    • 11 origin of all maximal supergravities. J. High Energy Phys. JHEP07 (2007) 063 arXiv:0705.0752 [hep-th]
    • (2007) J. High Energy Phys. , vol.JHEP07 , pp. 063
    • Riccioni, F.1    West, P.C.2
  • 64
    • 61549103575 scopus 로고    scopus 로고
    • P.P. Cook, P.C. West, Charge multiplets and masses for E(11). arXiv:0805.4451[hep-th]
    • P.P. Cook, P.C. West, Charge multiplets and masses for E(11). arXiv:0805.4451[hep-th]
  • 65
    • 2542536530 scopus 로고    scopus 로고
    • U-duality and central charges in various dimensions revisited
    • arXiv:hep-th/9612105
    • Andrianopoli L., D'Auria R., and Ferrara S. U-duality and central charges in various dimensions revisited. Internat. J. Modern Phys. A13 (1998) 431-490. arXiv:hep-th/9612105
    • (1998) Internat. J. Modern Phys. , vol.A13 , pp. 431-490
    • Andrianopoli, L.1    D'Auria, R.2    Ferrara, S.3
  • 66
    • 24944574778 scopus 로고    scopus 로고
    • Unitary realizations of U-duality groups as conformal and quasiconformal groups and extremal black holes of supergravity theories
    • arXiv:hep-th/0502235
    • Gunaydin M. Unitary realizations of U-duality groups as conformal and quasiconformal groups and extremal black holes of supergravity theories. AIP Conf. Proc. 767 (2005) 268-287. arXiv:hep-th/0502235
    • (2005) AIP Conf. Proc. , vol.767 , pp. 268-287
    • Gunaydin, M.1
  • 67
    • 0032484420 scopus 로고    scopus 로고
    • Gravitational duality, branes and charges
    • arXiv:hep-th/9705162
    • Hull C.M. Gravitational duality, branes and charges. Nuclear Phys. B509 (1998) 216-251. arXiv:hep-th/9705162
    • (1998) Nuclear Phys. , vol.B509 , pp. 216-251
    • Hull, C.M.1
  • 68
    • 61549135576 scopus 로고    scopus 로고
    • 6. arXiv:0804.0651 [hep-th]
    • 6. arXiv:0804.0651 [hep-th]
  • 69
    • 4243684526 scopus 로고    scopus 로고
    • Entanglement of formation of an arbitrary state of two qubits
    • arXiv:quant-ph/9709029
    • Wootters W.K. Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80 (1998) 2245-2248. arXiv:quant-ph/9709029
    • (1998) Phys. Rev. Lett. , vol.80 , pp. 2245-2248
    • Wootters, W.K.1
  • 70
    • 11744385893 scopus 로고    scopus 로고
    • Computing local invariants of qubit systems
    • arXiv:quant-ph/9712040
    • Grassl M., Rotteler M., and Beth T. Computing local invariants of qubit systems. Phys. Rev. A58 (1998) 1833-1839. arXiv:quant-ph/9712040
    • (1998) Phys. Rev. , vol.A58 , pp. 1833-1839
    • Grassl, M.1    Rotteler, M.2    Beth, T.3
  • 71
    • 0000799719 scopus 로고    scopus 로고
    • On multi-particle entanglement and its applications to cryptography
    • arXiv:quant-ph/9902036
    • Kempe J. On multi-particle entanglement and its applications to cryptography. Phys. Rev. A60 (1999) 910-916. arXiv:quant-ph/9902036
    • (1999) Phys. Rev. , vol.A60 , pp. 910-916
    • Kempe, J.1
  • 72
    • 0039032387 scopus 로고    scopus 로고
    • Exact and asymptotic measures of multipartite pure state entanglement
    • arXiv:quant-ph/9908073
    • C.H. Bennett, S. Popescu, D. Rohrlich, J.A. Smolin, A.V. Thapliyal, Exact and asymptotic measures of multipartite pure state entanglement. arXiv:quant-ph/9908073
    • Bennett, C.H.1    Popescu, S.2    Rohrlich, D.3    Smolin, J.A.4    Thapliyal, A.V.5
  • 73
    • 61549131381 scopus 로고    scopus 로고
    • Algebraic measures of entanglement
    • arXiv:quant-ph/0008031
    • J.-L. Brylinski, Algebraic measures of entanglement. arXiv:quant-ph/0008031
    • Brylinski, J.-L.1
  • 74
    • 61549118925 scopus 로고    scopus 로고
    • Invariant polynomial functions on k qudits
    • arXiv:quant-ph/0010101
    • J. Brylinski, R. Brylinski, Invariant polynomial functions on k qudits. arXiv:quant-ph/0010101
    • Brylinski, J.1    Brylinski, R.2
  • 75
    • 0035417517 scopus 로고    scopus 로고
    • A note on invariants and entanglements
    • arXiv:quant-ph/0109073
    • Albeverio S., and Fei S.-M. A note on invariants and entanglements. J. Opt. B Quantum. Semiclass. Opt. B3 (2001) 223-227. arXiv:quant-ph/0109073
    • (2001) J. Opt. B Quantum. Semiclass. Opt. , vol.B3 , pp. 223-227
    • Albeverio, S.1    Fei, S.-M.2
  • 76
    • 0034697925 scopus 로고    scopus 로고
    • Local symmetry properties of pure 3-qubit states
    • arXiv:quant-ph/0001091
    • Carteret H., and Sudbery A. Local symmetry properties of pure 3-qubit states. J. Phys. A 33 (2000) 4981. arXiv:quant-ph/0001091
    • (2000) J. Phys. A , vol.33 , pp. 4981
    • Carteret, H.1    Sudbery, A.2
  • 77
    • 0034356504 scopus 로고    scopus 로고
    • Multipartite generalisation of the Schmidt decomposition
    • arXiv:quant-ph/0006125
    • Carteret H., Higuchi A., and Sudbery A. Multipartite generalisation of the Schmidt decomposition. J. Math. Phys. 41 (2000) 7932. arXiv:quant-ph/0006125
    • (2000) J. Math. Phys. , vol.41 , pp. 7932
    • Carteret, H.1    Higuchi, A.2    Sudbery, A.3
  • 78
    • 0141573313 scopus 로고    scopus 로고
    • Normal forms and entanglement measures for multipartite quantum states
    • arXiv:quant-ph/0105090
    • Verstraete F., Dehaene J., and De Moor B. Normal forms and entanglement measures for multipartite quantum states. Phys. Rev. A68 (2003) 012103. arXiv:quant-ph/0105090
    • (2003) Phys. Rev. , vol.A68 , pp. 012103
    • Verstraete, F.1    Dehaene, J.2    De Moor, B.3
  • 79
    • 1142277203 scopus 로고    scopus 로고
    • The geometry of entanglement: Metrics, connections and the geometric phase
    • arXiv:quant-ph/0306115
    • Levay P. The geometry of entanglement: Metrics, connections and the geometric phase. J. Phys. A37 (2004) 1821-1842. arXiv:quant-ph/0306115
    • (2004) J. Phys. , vol.A37 , pp. 1821-1842
    • Levay, P.1
  • 80
    • 61549117977 scopus 로고    scopus 로고
    • Unitary invariants of qubit systems
    • arXiv:quant-ph/0604202
    • F. Toumazet, J. Luque, J. Thibon, Unitary invariants of qubit systems. arXiv:quant-ph/0604202
    • Toumazet, F.1    Luque, J.2    Thibon, J.3
  • 81
    • 34347329145 scopus 로고    scopus 로고
    • Bipartite entanglement measure based on covariances
    • arXiv:quant-ph/0703249
    • Abascal I.S., and Bjork G. Bipartite entanglement measure based on covariances. Phys. Rev. A 75 (2007) 062317. arXiv:quant-ph/0703249
    • (2007) Phys. Rev. A , vol.75 , pp. 062317
    • Abascal, I.S.1    Bjork, G.2
  • 82
    • 33750896329 scopus 로고    scopus 로고
    • An introduction to entanglement measures
    • arXiv:quant-ph/0504163
    • Plenio M.B., and Virmani S. An introduction to entanglement measures. Quantum. Inf. Comput. 7 (2007) 1. arXiv:quant-ph/0504163
    • (2007) Quantum. Inf. Comput. , vol.7 , pp. 1
    • Plenio, M.B.1    Virmani, S.2
  • 83
    • 43849112312 scopus 로고    scopus 로고
    • Entanglement in many-body systems
    • arXiv:quant-ph/0703044
    • Amico L., Fazio R., Osterloh A., and Vedral V. Entanglement in many-body systems. Rev. Modern Phys. 80 (2008) 517-576. arXiv:quant-ph/0703044
    • (2008) Rev. Modern Phys. , vol.80 , pp. 517-576
    • Amico, L.1    Fazio, R.2    Osterloh, A.3    Vedral, V.4
  • 86
    • 0002409705 scopus 로고
    • A Duality between strings and five-branes
    • Duff M.J., and Lu J.X. A Duality between strings and five-branes. Classical Quantum Gravity 9 (1992) 1-16
    • (1992) Classical Quantum Gravity , vol.9 , pp. 1-16
    • Duff, M.J.1    Lu, J.X.2
  • 87
    • 0542408276 scopus 로고
    • String solitons
    • arXiv:hep-th/9412184
    • Duff M.J., Khuri R.R., and Lu J.X. String solitons. Phys. Rep. 259 (1995) 213-326. arXiv:hep-th/9412184
    • (1995) Phys. Rep. , vol.259 , pp. 213-326
    • Duff, M.J.1    Khuri, R.R.2    Lu, J.X.3
  • 88
    • 0003878507 scopus 로고    scopus 로고
    • TASI lectures on black holes in string theory
    • arXiv:hep-th/0008241
    • A.W. Peet, TASI lectures on black holes in string theory. arXiv:hep-th/0008241
    • Peet, A.W.1
  • 89
    • 0031234460 scopus 로고    scopus 로고
    • Black holes and critical points in moduli space
    • arXiv:hep-th/9702103
    • Ferrara S., Gibbons G.W., and Kallosh R. Black holes and critical points in moduli space. Nuclear Phys. B500 (1997) 75-93. arXiv:hep-th/9702103
    • (1997) Nuclear Phys. , vol.B500 , pp. 75-93
    • Ferrara, S.1    Gibbons, G.W.2    Kallosh, R.3
  • 90
    • 61549120890 scopus 로고    scopus 로고
    • F.A. Bais, J. Doyne Farmer, The physics of information. arXiv:0708.2837 [physics.class-ph]
    • F.A. Bais, J. Doyne Farmer, The physics of information. arXiv:0708.2837 [physics.class-ph]
  • 91
    • 0000486090 scopus 로고
    • On the Einstein-Podolsky-Rosen paradox
    • Bell J.S. On the Einstein-Podolsky-Rosen paradox. Physics 1 (1964) 195
    • (1964) Physics , vol.1 , pp. 195
    • Bell, J.S.1
  • 92
    • 0003864761 scopus 로고
    • Prentice-Hall, Englewood Cliffs, NJ
    • Bohm D. Quantum Theory (1951), Prentice-Hall, Englewood Cliffs, NJ
    • (1951) Quantum Theory
    • Bohm, D.1
  • 93
    • 33947385649 scopus 로고
    • Can quantum mechanical description of physical reality be considered complete?
    • Einstein A., Podolsky B., and Rosen N. Can quantum mechanical description of physical reality be considered complete?. Phys. Rev. 47 (1935) 777-780
    • (1935) Phys. Rev. , vol.47 , pp. 777-780
    • Einstein, A.1    Podolsky, B.2    Rosen, N.3
  • 94
    • 61549118305 scopus 로고
    • schilpp P.A. (Ed), Cambridge University Press
    • Einstein A. In: schilpp P.A. (Ed). Autobiographical notes in albert Einstein: Philosopher-scientist. Library of Living Philosophers vol. 3 (1970), Cambridge University Press
    • (1970) Library of Living Philosophers , vol.3
    • Einstein, A.1
  • 95
    • 0000617612 scopus 로고
    • Quantum mysteries revisited
    • Mermin N.D. Quantum mysteries revisited. Am. J. Phys. 58 (1990) 731-734
    • (1990) Am. J. Phys. , vol.58 , pp. 731-734
    • Mermin, N.D.1
  • 96
    • 33746434120 scopus 로고    scopus 로고
    • In praise of measurement
    • arXiv:quant-ph/0612216
    • Mermin N.D. In praise of measurement. Quantum Inf. Process. 5 (2006) 239. arXiv:quant-ph/0612216
    • (2006) Quantum Inf. Process. , vol.5 , pp. 239
    • Mermin, N.D.1
  • 99
    • 34848880433 scopus 로고    scopus 로고
    • The slocc invariant and the residual entanglement for n-qubits
    • arXiv:0704.2087 [quant-ph]
    • Li D., Huang H., and Li X. The slocc invariant and the residual entanglement for n-qubits. Phys. Rev. A 76 (2007) 032304 arXiv:0704.2087 [quant-ph]
    • (2007) Phys. Rev. A , vol.76 , pp. 032304
    • Li, D.1    Huang, H.2    Li, X.3
  • 100
    • 33751542734 scopus 로고    scopus 로고
    • Inductive classification of multipartite entanglement under slocc
    • arXiv:quant-ph/0603243
    • Lamata L., Leon J., Salgado D., and Solano E. Inductive classification of multipartite entanglement under slocc. Phys. Rev. A 74 (2006) 052336. arXiv:quant-ph/0603243
    • (2006) Phys. Rev. A , vol.74 , pp. 052336
    • Lamata, L.1    Leon, J.2    Salgado, D.3    Solano, E.4
  • 101
    • 0032325885 scopus 로고    scopus 로고
    • On multi-particle entanglement
    • arXiv:quant-ph/9711016
    • Linden N., and Popescu S. On multi-particle entanglement. Fortschr. Phys. 46 (1998) 567-578. arXiv:quant-ph/9711016
    • (1998) Fortschr. Phys. , vol.46 , pp. 567-578
    • Linden, N.1    Popescu, S.2
  • 102
    • 0000953494 scopus 로고    scopus 로고
    • Three qubits can be entangled in two inequivalent ways
    • arXiv:quant-ph/0005115
    • Dür W., Vidal G., and Cirac J.I. Three qubits can be entangled in two inequivalent ways. Phys. Rev. A62 (2000) 062314. arXiv:quant-ph/0005115
    • (2000) Phys. Rev. , vol.A62 , pp. 062314
    • Dür, W.1    Vidal, G.2    Cirac, J.I.3
  • 103
    • 0035951745 scopus 로고    scopus 로고
    • On local invariants of pure three-qubit states
    • arXiv:quant-ph/0001116
    • Sudbery A. On local invariants of pure three-qubit states. J. Phys. A34 (2001) 643-652. arXiv:quant-ph/0001116
    • (2001) J. Phys. , vol.A34 , pp. 643-652
    • Sudbery, A.1
  • 104
    • 61549131527 scopus 로고    scopus 로고
    • Properties of entanglement monotones for three-qubit pure states
    • arXiv:quant-ph/0106042
    • R. Gingrich, Properties of entanglement monotones for three-qubit pure states. arXiv:quant-ph/0106042
    • Gingrich, R.1
  • 105
    • 33746326137 scopus 로고    scopus 로고
    • Entanglement monotones and maximally entangled states in multipartite qubit systems
    • arXiv:quant-ph/0506073
    • Osterloh A., and Siewert J. Entanglement monotones and maximally entangled states in multipartite qubit systems. Int. J. Quantum. Inf. 4 (2006) 531. arXiv:quant-ph/0506073
    • (2006) Int. J. Quantum. Inf. , vol.4 , pp. 531
    • Osterloh, A.1    Siewert, J.2
  • 106
    • 0034652055 scopus 로고    scopus 로고
    • On the characterization of entanglement
    • arXiv:quant-ph/9807077
    • Vidal G. On the characterization of entanglement. J. Mod. Opt. 47 (2000) 355. arXiv:quant-ph/9807077
    • (2000) J. Mod. Opt. , vol.47 , pp. 355
    • Vidal, G.1
  • 107
    • 25844498536 scopus 로고    scopus 로고
    • On the geometry of a class of n-qubit entanglement monotones
    • arXiv:quant-ph/0507070
    • Levay P. On the geometry of a class of n-qubit entanglement monotones. J. Phys. A 38 (2005) 9075. arXiv:quant-ph/0507070
    • (2005) J. Phys. A , vol.38 , pp. 9075
    • Levay, P.1
  • 108
    • 61549110769 scopus 로고    scopus 로고
    • P. Gibbs, Diophantine quadruples and Cayley's hyperdeterminant. arXiv:math/0107203
    • P. Gibbs, Diophantine quadruples and Cayley's hyperdeterminant. arXiv:math/0107203
  • 109
    • 61549123138 scopus 로고    scopus 로고
    • Singular 2 × 2 × 2 Arrays, Oxford
    • preprint
    • K.V. Fernando, Singular 2 × 2 × 2 Arrays, Oxford, preprint
    • Fernando, K.V.1
  • 110
    • 34250836479 scopus 로고    scopus 로고
    • Entanglement of three-qubit geometry
    • arXiv:quant-ph/0612117
    • Brody D.C., Gustavsson A.C.T., and Hughston L.P. Entanglement of three-qubit geometry. Conf. Ser. 67 (2007) 012044. arXiv:quant-ph/0612117
    • (2007) Conf. Ser. , vol.67 , pp. 012044
    • Brody, D.C.1    Gustavsson, A.C.T.2    Hughston, L.P.3
  • 111
    • 33244462176 scopus 로고    scopus 로고
    • Entanglement of three-qubit pure states in terms of teleportation capability
    • arXiv:quant-ph/0502157
    • Lee S., Joo J., and Kim J. Entanglement of three-qubit pure states in terms of teleportation capability. Phys. Rev. A 72 (2005) 024302. arXiv:quant-ph/0502157
    • (2005) Phys. Rev. A , vol.72 , pp. 024302
    • Lee, S.1    Joo, J.2    Kim, J.3
  • 112
    • 61549099451 scopus 로고    scopus 로고
    • Teleportation capability, distillability, and nonlocality on three-qubit states
    • arXiv:quant-ph/0702247
    • S. Lee, J. Joo, J. Kim, Teleportation capability, distillability, and nonlocality on three-qubit states. arXiv:quant-ph/0702247
    • Lee, S.1    Joo, J.2    Kim, J.3
  • 113
    • 0037243640 scopus 로고    scopus 로고
    • Classification of multipartite entangled states by multidimensional determinants
    • arXiv:quant-ph/0206111
    • Miyake A. Classification of multipartite entangled states by multidimensional determinants. Phys. Rev. A 67 (2003) 012108. arXiv:quant-ph/0206111
    • (2003) Phys. Rev. A , vol.67 , pp. 012108
    • Miyake, A.1
  • 114
    • 61549085112 scopus 로고    scopus 로고
    • Algebraic invariants of five qubits
    • arXiv:quant-ph/0506058
    • J. Luque, J.-Y. Thibon, Algebraic invariants of five qubits. arXiv:quant-ph/0506058
    • Luque, J.1    Thibon, J.-Y.2
  • 115
    • 0347090655 scopus 로고    scopus 로고
    • Three-qubit pure-state canonical forms
    • arXiv:quant-ph/0009107
    • Acin A., Andrianov A., Jane E., and Tarrach R. Three-qubit pure-state canonical forms. J. Phys. A 34 (2001) 6725. arXiv:quant-ph/0009107
    • (2001) J. Phys. A , vol.34 , pp. 6725
    • Acin, A.1    Andrianov, A.2    Jane, E.3    Tarrach, R.4
  • 118
    • 0038284569 scopus 로고    scopus 로고
    • Generalized Schmidt decomposition and classification of three-quantum-bit states
    • arXiv:quant-ph/0003050
    • Acin A., Andrianov A., Costa L., Jane E., Latorre J., and Tarrach R. Generalized Schmidt decomposition and classification of three-quantum-bit states. Phys. Rev. Lett. 85 (2000) 1560. arXiv:quant-ph/0003050
    • (2000) Phys. Rev. Lett. , vol.85 , pp. 1560
    • Acin, A.1    Andrianov, A.2    Costa, L.3    Jane, E.4    Latorre, J.5    Tarrach, R.6
  • 119
    • 0037432922 scopus 로고    scopus 로고
    • Quantify entanglement by concurrence hierarchy
    • arXiv:quant-ph/0204041
    • Fan H., Matsumoto K., and Imai H. Quantify entanglement by concurrence hierarchy. J. Phys. A: Math. Gen. 36 (2003) 4151-4158. arXiv:quant-ph/0204041
    • (2003) J. Phys. A: Math. Gen. , vol.36 , pp. 4151-4158
    • Fan, H.1    Matsumoto, K.2    Imai, H.3
  • 120
    • 24144478109 scopus 로고    scopus 로고
    • Degree of entanglement for two qutrits in a pure state
    • arXiv:quant-ph/0305043
    • J.L. Cereceda, Degree of entanglement for two qutrits in a pure state. arXiv:quant-ph/0305043
    • Cereceda, J.L.1
  • 121
    • 61549084786 scopus 로고    scopus 로고
    • Generalized concurrence and limits of separability for two qutrits
    • arXiv:quant-ph/0507223
    • C. Herreno-Fierro, J. Luthra, Generalized concurrence and limits of separability for two qutrits. arXiv:quant-ph/0507223
    • Herreno-Fierro, C.1    Luthra, J.2
  • 122
    • 33744551119 scopus 로고    scopus 로고
    • Classification and quantification of entangled bipartite qutrit pure states
    • arXiv:quant-ph/0510178
    • Pan F., Lu G., and Draayer J. Classification and quantification of entangled bipartite qutrit pure states. Internat. J. Modern Phys. B 20 (2006) 1333. arXiv:quant-ph/0510178
    • (2006) Internat. J. Modern Phys. B , vol.20 , pp. 1333
    • Pan, F.1    Lu, G.2    Draayer, J.3
  • 123
    • 61549083537 scopus 로고    scopus 로고
    • Negativity and concurrence for two qutrits
    • arXiv:quant-ph/0507263
    • S. Rai, J.R. Luthra, Negativity and concurrence for two qutrits. arXiv:quant-ph/0507263
    • Rai, S.1    Luthra, J.R.2
  • 124
    • 0000075120 scopus 로고
    • Dual pairs of type II string compactification
    • arXiv:hep-th/9508064
    • Sen A., and Vafa C. Dual pairs of type II string compactification. Nuclear Phys. B455 (1995) 165-187. arXiv:hep-th/9508064
    • (1995) Nuclear Phys. , vol.B455 , pp. 165-187
    • Sen, A.1    Vafa, C.2
  • 125
    • 0033606747 scopus 로고    scopus 로고
    • Non-perturbative triality in heterotic and type II N = 2 strings
    • arXiv:hep-th/9901117
    • Gregori A., Kounnas C., and Petropoulos P.M. Non-perturbative triality in heterotic and type II N = 2 strings. Nuclear Phys. B553 (1999) 108-132. arXiv:hep-th/9901117
    • (1999) Nuclear Phys. , vol.B553 , pp. 108-132
    • Gregori, A.1    Kounnas, C.2    Petropoulos, P.M.3
  • 126
    • 0000097485 scopus 로고    scopus 로고
    • Dyonic BPS saturated black holes of heterotic string on a six torus
    • arXiv:hep-th/9507090
    • Cvetic M., and Youm D. Dyonic BPS saturated black holes of heterotic string on a six torus. Phys. Rev. D53 (1996) 584-588. arXiv:hep-th/9507090
    • (1996) Phys. Rev. , vol.D53 , pp. 584-588
    • Cvetic, M.1    Youm, D.2
  • 127
    • 0004334538 scopus 로고    scopus 로고
    • On electromagnetic duality in locally supersymmetric N = 2 Yang-Mills theory
    • arXiv:hep-th/9412200
    • A. Ceresole, R. D'Auria, S. Ferrara, A. Van Proeyen, On electromagnetic duality in locally supersymmetric N = 2 Yang-Mills theory. arXiv:hep-th/9412200
    • Ceresole, A.1    D'Auria, R.2    Ferrara, S.3    Van Proeyen, A.4
  • 128
    • 4243306443 scopus 로고
    • N = 2 extremal black holes
    • arXiv:hep-th/9508072
    • Ferrara S., Kallosh R., and Strominger A. N = 2 extremal black holes. Phys. Rev. D52 (1995) 5412-5416. arXiv:hep-th/9508072
    • (1995) Phys. Rev. , vol.D52 , pp. 5412-5416
    • Ferrara, S.1    Kallosh, R.2    Strominger, A.3
  • 129
    • 0242297832 scopus 로고    scopus 로고
    • Geometry of the 3-qubit state, entanglement and division algebras
    • arXiv:quant-ph/0302081
    • Bernevig B.A., and Chen H.-D. Geometry of the 3-qubit state, entanglement and division algebras. J. Phys. A: Math. Gen. 36 (2003) 8325. arXiv:quant-ph/0302081
    • (2003) J. Phys. A: Math. Gen. , vol.36 , pp. 8325
    • Bernevig, B.A.1    Chen, H.-D.2
  • 130
    • 18544378280 scopus 로고    scopus 로고
    • Geometry of three-qubit entanglement
    • arXiv:arXiv:quant-ph/0403060
    • Lévay P. Geometry of three-qubit entanglement. Phys. Rev. A71 Jan (2005) 012334-+. arXiv:arXiv:quant-ph/0403060
    • (2005) Phys. Rev. , vol.A71 , Issue.Jan
    • Lévay, P.1
  • 131
    • 33744748026 scopus 로고    scopus 로고
    • DeSitter entropy, quantum entanglement and AdS/CFT
    • arXiv:hep-th/0002145
    • Hawking S., Maldacena J.M., and Strominger A. DeSitter entropy, quantum entanglement and AdS/CFT. J. High Energy Phys. JHEP05 (2001) 001. arXiv:hep-th/0002145
    • (2001) J. High Energy Phys. , vol.JHEP05 , pp. 001
    • Hawking, S.1    Maldacena, J.M.2    Strominger, A.3
  • 132
    • 0003817618 scopus 로고    scopus 로고
    • Lectures on superconformal quantum mechanics and multi- black hole moduli spaces
    • arXiv:hep-th/9911066
    • R. Britto-Pacumio, J. Michelson, A. Strominger, A. Volovich, Lectures on superconformal quantum mechanics and multi- black hole moduli spaces. arXiv:hep-th/9911066
    • Britto-Pacumio, R.1    Michelson, J.2    Strominger, A.3    Volovich, A.4
  • 133
    • 0037741393 scopus 로고    scopus 로고
    • Understanding quantum entanglement: Qubits, rebits and the quaternionic approach
    • arXiv:quant-ph/0603060
    • Batle J., Plastino A.R., Casas M., and Plastino A. Understanding quantum entanglement: Qubits, rebits and the quaternionic approach. Optics Spectroscopy 94 (2003) 700. arXiv:quant-ph/0603060
    • (2003) Optics Spectroscopy , vol.94 , pp. 700
    • Batle, J.1    Plastino, A.R.2    Casas, M.3    Plastino, A.4
  • 134
    • 61549130725 scopus 로고    scopus 로고
    • Entanglement of formation of an arbitrary state of two rebits
    • arXiv:quant-ph/0009063
    • C.M. Caves, C.A. Fuchs, C.A. Rungta, Entanglement of formation of an arbitrary state of two rebits. arXiv:quant-ph/0009063
    • Caves, C.M.1    Fuchs, C.A.2    Rungta, C.A.3
  • 135
    • 0000795648 scopus 로고
    • Massive string states as extreme black holes
    • arXiv:hep-th/9406105
    • Duff M.J., and Rahmfeld J. Massive string states as extreme black holes. Phys. Lett. B345 (1995) 441-447. arXiv:hep-th/9406105
    • (1995) Phys. Lett. , vol.B345 , pp. 441-447
    • Duff, M.J.1    Rahmfeld, J.2
  • 136
    • 0000432852 scopus 로고    scopus 로고
    • Bound states of black holes and other P-branes
    • arXiv:hep-th/9605085
    • Duff M.J., and Rahmfeld J. Bound states of black holes and other P-branes. Nuclear Phys. B481 (1996) 332-352. arXiv:hep-th/9605085
    • (1996) Nuclear Phys. , vol.B481 , pp. 332-352
    • Duff, M.J.1    Rahmfeld, J.2
  • 137
    • 33749156290 scopus 로고    scopus 로고
    • From BPS to non-BPS black holes canonically
    • arXiv:hep-th/0603003
    • R. Kallosh, From BPS to non-BPS black holes canonically. arXiv:hep-th/0603003
    • Kallosh, R.1
  • 138
    • 38949214167 scopus 로고    scopus 로고
    • Black holes in supergravity: The non-BPS branch
    • arXiv:0710.4967 [hep-th]
    • Gimon E.G., Larsen F., and Simon J. Black holes in supergravity: The non-BPS branch. J. High Energy Phys. JHEP01 (2008) 040 arXiv:0710.4967 [hep-th]
    • (2008) J. High Energy Phys. , vol.JHEP01 , pp. 040
    • Gimon, E.G.1    Larsen, F.2    Simon, J.3
  • 139
    • 0001110927 scopus 로고
    • Strings, black holes and Lorentz contraction
    • arXiv:hep-th/9308139
    • Susskind L. Strings, black holes and Lorentz contraction. Phys. Rev. D49 (1994) 6606-6611. arXiv:hep-th/9308139
    • (1994) Phys. Rev. , vol.D49 , pp. 6606-6611
    • Susskind, L.1
  • 140
    • 0011508219 scopus 로고
    • Black hole solutions in heterotic string theory on a torus
    • arXiv:hep-th/9411187
    • Sen A. Black hole solutions in heterotic string theory on a torus. Nuclear Phys. B440 (1995) 421-440. arXiv:hep-th/9411187
    • (1995) Nuclear Phys. , vol.B440 , pp. 421-440
    • Sen, A.1
  • 141
    • 0001513742 scopus 로고
    • Extremal black holes and elementary string states
    • arXiv:hep-th/9504147
    • Sen A. Extremal black holes and elementary string states. Modern Phys. Lett. A10 (1995) 2081-2094. arXiv:hep-th/9504147
    • (1995) Modern Phys. Lett. , vol.A10 , pp. 2081-2094
    • Sen, A.1
  • 142
    • 21444441609 scopus 로고    scopus 로고
    • A stringy cloak for a classical singularity
    • arXiv:hep-th/0410076
    • Dabholkar A., Kallosh R., and Maloney A. A stringy cloak for a classical singularity. J. High Energy Phys. JHEP12 (2004) 059. arXiv:hep-th/0410076
    • (2004) J. High Energy Phys. , vol.JHEP12 , pp. 059
    • Dabholkar, A.1    Kallosh, R.2    Maloney, A.3
  • 143
    • 33646422739 scopus 로고    scopus 로고
    • Extremal single-charge small black holes: Entropy function analysis
    • arXiv:hep-th/0601183
    • Sinha A., and Suryanarayana N.V. Extremal single-charge small black holes: Entropy function analysis. Classical Quantum Gravity 23 (2006) 3305-3322. arXiv:hep-th/0601183
    • (2006) Classical Quantum Gravity , vol.23 , pp. 3305-3322
    • Sinha, A.1    Suryanarayana, N.V.2
  • 144
    • 42749098628 scopus 로고    scopus 로고
    • Black hole attractors and the topological string
    • arXiv:hep-th/0405146
    • Ooguri H., Strominger A., and Vafa C. Black hole attractors and the topological string. Phys. Rev. D70 (2004) 106007. arXiv:hep-th/0405146
    • (2004) Phys. Rev. , vol.D70 , pp. 106007
    • Ooguri, H.1    Strominger, A.2    Vafa, C.3
  • 145
    • 27544458480 scopus 로고    scopus 로고
    • Precision counting of small black holes
    • arXiv:hep-th/0507014
    • Dabholkar A., Denef F., Moore G.W., and Pioline B. Precision counting of small black holes. J. High Energy Phys. JHEP10 (2005) 096. arXiv:hep-th/0507014
    • (2005) J. High Energy Phys. , vol.JHEP10 , pp. 096
    • Dabholkar, A.1    Denef, F.2    Moore, G.W.3    Pioline, B.4
  • 147
    • 33846218742 scopus 로고    scopus 로고
    • New attractor, entropy function and black hole partition function
    • arXiv:hep-th/0605279
    • Alishahiha M., and Ebrahim H. New attractor, entropy function and black hole partition function. J. High Energy Phys. JHEP11 (2006) 017. arXiv:hep-th/0605279
    • (2006) J. High Energy Phys. , vol.JHEP11 , pp. 017
    • Alishahiha, M.1    Ebrahim, H.2
  • 148
    • 0002098396 scopus 로고    scopus 로고
    • Macroscopic entropy of N = 2 extremal black holes
    • arXiv:hep-th/9602111
    • Strominger A. Macroscopic entropy of N = 2 extremal black holes. Phys. Lett. B383 (1996) 39-43. arXiv:hep-th/9602111
    • (1996) Phys. Lett. , vol.B383 , pp. 39-43
    • Strominger, A.1
  • 149
    • 0043054483 scopus 로고    scopus 로고
    • Supersymmetry and attractors
    • arXiv:hep-th/9602136
    • Ferrara S., and Kallosh R. Supersymmetry and attractors. Phys. Rev. D54 (1996) 1514-1524. arXiv:hep-th/9602136
    • (1996) Phys. Rev. , vol.D54 , pp. 1514-1524
    • Ferrara, S.1    Kallosh, R.2
  • 150
    • 33750434304 scopus 로고    scopus 로고
    • Charge orbits of symmetric special geometries and attractors
    • arXiv:hep-th/0606209
    • Bellucci S., Ferrara S., Gunaydin M., and Marrani A. Charge orbits of symmetric special geometries and attractors. Internat. J. Modern Phys. A21 (2006) 5043-5098. arXiv:hep-th/0606209
    • (2006) Internat. J. Modern Phys. , vol.A21 , pp. 5043-5098
    • Bellucci, S.1    Ferrara, S.2    Gunaydin, M.3    Marrani, A.4
  • 151
    • 34547606677 scopus 로고    scopus 로고
    • Attractor horizon geometries of extremal black holes
    • arXiv:hep-th/0702019
    • S. Bellucci, S. Ferrara, A. Marrani, Attractor horizon geometries of extremal black holes. arXiv:hep-th/0702019
    • Bellucci, S.1    Ferrara, S.2    Marrani, A.3
  • 152
    • 33645681704 scopus 로고    scopus 로고
    • Non-supersymmetric attractors in string theory
    • arXiv:hep-th/0511117
    • Tripathy P.K., and Trivedi S.P. Non-supersymmetric attractors in string theory. J. High Energy Phys. JHEP03 (2006) 022. arXiv:hep-th/0511117
    • (2006) J. High Energy Phys. , vol.JHEP03 , pp. 022
    • Tripathy, P.K.1    Trivedi, S.P.2
  • 153
    • 33645662750 scopus 로고    scopus 로고
    • The non-BPS black hole attractor equation
    • arXiv:hep-th/0602005
    • Kallosh R., Sivanandam N., and Soroush M. The non-BPS black hole attractor equation. J. High Energy Phys. JHEP03 (2006) 060. arXiv:hep-th/0602005
    • (2006) J. High Energy Phys. , vol.JHEP03 , pp. 060
    • Kallosh, R.1    Sivanandam, N.2    Soroush, M.3
  • 154
    • 0001143510 scopus 로고    scopus 로고
    • Branes at angles and black holes
    • arXiv:hep-th/9704143
    • Balasubramanian V., Larsen F., and Leigh R.G. Branes at angles and black holes. Phys. Rev. D57 (1998) 3509-3528. arXiv:hep-th/9704143
    • (1998) Phys. Rev. , vol.D57 , pp. 3509-3528
    • Balasubramanian, V.1    Larsen, F.2    Leigh, R.G.3
  • 155
    • 0035620746 scopus 로고    scopus 로고
    • Conformal and quasiconformal realizations of exceptional Lie groups
    • arXiv:hep-th/0008063
    • Gunaydin M., Koepsell K., and Nicolai H. Conformal and quasiconformal realizations of exceptional Lie groups. Comm. Math. Phys. 221 (2001) 57-76. arXiv:hep-th/0008063
    • (2001) Comm. Math. Phys. , vol.221 , pp. 57-76
    • Gunaydin, M.1    Koepsell, K.2    Nicolai, H.3
  • 156
    • 1542459047 scopus 로고    scopus 로고
    • E(7) symmetric area of the black hole horizon
    • arXiv:hep-th/9602014
    • Kallosh R., and Kol B. E(7) symmetric area of the black hole horizon. Phys. Rev. D53 (1996) 5344-5348. arXiv:hep-th/9602014
    • (1996) Phys. Rev. , vol.D53 , pp. 5344-5348
    • Kallosh, R.1    Kol, B.2
  • 157
    • 0032395187 scopus 로고    scopus 로고
    • Branes, central charges and U-duality invariant BPS conditions
    • arXiv:hep-th/9706097
    • Ferrara S., and Maldacena J.M. Branes, central charges and U-duality invariant BPS conditions. Classical Quantum Gravity 15 (1998) 749-758. arXiv:hep-th/9706097
    • (1998) Classical Quantum Gravity , vol.15 , pp. 749-758
    • Ferrara, S.1    Maldacena, J.M.2
  • 158
    • 0030597908 scopus 로고    scopus 로고
    • All the static spherically symmetric black holes of heterotic string on a six torus
    • arXiv:hep-th/9512127
    • Cvetic M., and Youm D. All the static spherically symmetric black holes of heterotic string on a six torus. Nuclear Phys. B472 (1996) 249-267. arXiv:hep-th/9512127
    • (1996) Nuclear Phys. , vol.B472 , pp. 249-267
    • Cvetic, M.1    Youm, D.2
  • 159
    • 0009211932 scopus 로고    scopus 로고
    • Solitonic strings and BPS saturated dyonic black holes
    • arXiv:hep-th/9512031
    • Cvetic M., and Tseytlin A.A. Solitonic strings and BPS saturated dyonic black holes. Phys. Rev. D53 (1996) 5619-5633. arXiv:hep-th/9512031
    • (1996) Phys. Rev. , vol.D53 , pp. 5619-5633
    • Cvetic, M.1    Tseytlin, A.A.2
  • 160
    • 0030602109 scopus 로고    scopus 로고
    • Black holes and U-duality
    • arXiv:hep-th/9606193
    • Cvetic M., and Hull C.M. Black holes and U-duality. Nuclear Phys. B480 (1996) 296-316. arXiv:hep-th/9606193
    • (1996) Nuclear Phys. , vol.B480 , pp. 296-316
    • Cvetic, M.1    Hull, C.M.2
  • 161
    • 0033240887 scopus 로고    scopus 로고
    • The generating solution of regular N = 8 BPS black holes
    • arXiv:hep-th/9905143
    • Bertolini M., Fre P., and Trigiante M. The generating solution of regular N = 8 BPS black holes. Classical Quantum Gravity 16 (1999) 2987-3004. arXiv:hep-th/9905143
    • (1999) Classical Quantum Gravity , vol.16 , pp. 2987-3004
    • Bertolini, M.1    Fre, P.2    Trigiante, M.3
  • 162
    • 61549131062 scopus 로고
    • Editions du Centre National de la Recherche Scientifique
    • E. Cartan, Œeuvres complètes, Editions du Centre National de la Recherche Scientifique, 1984
    • (1984) Œeuvres complètes
    • Cartan, E.1
  • 163
    • 0035997407 scopus 로고    scopus 로고
    • The Octonions
    • arXiv:math/0105155
    • Baez J.C. The Octonions. Bull. Am. Math. Soc. 39 (2002) 145-205. arXiv:math/0105155
    • (2002) Bull. Am. Math. Soc. , vol.39 , pp. 145-205
    • Baez, J.C.1
  • 164
    • 22244493073 scopus 로고    scopus 로고
    • Octonionic representations of Clifford algebras and triality
    • arXiv:hep-th/9407179
    • J. Schray, C.A. Manogue, Octonionic representations of Clifford algebras and triality. arXiv:hep-th/9407179
    • Schray, J.1    Manogue, C.A.2
  • 166
    • 0033241184 scopus 로고    scopus 로고
    • Matrix representation of octonions and generalizations
    • arXiv:hep-th/9906065
    • Daboul J., and Delbourgo R. Matrix representation of octonions and generalizations. J. Math. Phys. 40 (1999) 4134-4150. arXiv:hep-th/9906065
    • (1999) J. Math. Phys. , vol.40 , pp. 4134-4150
    • Daboul, J.1    Delbourgo, R.2
  • 168
    • 0011763239 scopus 로고    scopus 로고
    • The exceptional Jordan algebra and the matrix string
    • arXiv:hep-th/0104050
    • L. Smolin, The exceptional Jordan algebra and the matrix string. arXiv:hep-th/0104050
    • Smolin, L.1
  • 169
    • 84901420243 scopus 로고    scopus 로고
    • On the octonionic M-superalgebra
    • arXiv:hep-th/0301163
    • F. Toppan, On the octonionic M-superalgebra. arXiv:hep-th/0301163
    • Toppan, F.1
  • 170
    • 61549125508 scopus 로고    scopus 로고
    • H. Albuquerque, S. Majid, Quasialgebra structure of the octonions. arXiv:math/9802116
    • H. Albuquerque, S. Majid, Quasialgebra structure of the octonions. arXiv:math/9802116
  • 171
    • 0005871295 scopus 로고    scopus 로고
    • Octonionic mobius transformations
    • arXiv:math-ph/9905024
    • Manogue C.A., and Dray T. Octonionic mobius transformations. Modern Phys. Lett. A14 (1999) 1243. arXiv:math-ph/9905024
    • (1999) Modern Phys. Lett. , vol.A14 , pp. 1243
    • Manogue, C.A.1    Dray, T.2
  • 172
    • 36248930275 scopus 로고
    • Quark structure and octonions
    • Günaydin M., and Gürsey F. Quark structure and octonions. J. Math. Phys. 14 Nov (1973) 1651-1667
    • (1973) J. Math. Phys. , vol.14 , Issue.Nov , pp. 1651-1667
    • Günaydin, M.1    Gürsey, F.2
  • 173
    • 0009099792 scopus 로고
    • Supersymmetry and the division algebras
    • Kugo T., and Townsend P.K. Supersymmetry and the division algebras. Nuclear Phys. B221 (1983) 357
    • (1983) Nuclear Phys. , vol.B221 , pp. 357
    • Kugo, T.1    Townsend, P.K.2
  • 174
    • 0035976873 scopus 로고    scopus 로고
    • Geometry of entangled states, Bloch spheres and Hopf fibrations
    • arXiv:quant-ph/0108137
    • Mosseri R., and Dandoloff R. Geometry of entangled states, Bloch spheres and Hopf fibrations. J. Phys. A34 (2001) 10243-10245. arXiv:quant-ph/0108137
    • (2001) J. Phys. , vol.A34 , pp. 10243-10245
    • Mosseri, R.1    Dandoloff, R.2
  • 175
    • 61549092912 scopus 로고    scopus 로고
    • Two-qubits and three qubit geometry and Hopf fibrations
    • Topology in Condensed Matter. Monastyrsky M.I. (Ed) Presented at the Dresde (Germany) "Topology in Condensed Matter Physics" colloquium in June 2002
    • Mosseri R. Two-qubits and three qubit geometry and Hopf fibrations. In: Monastyrsky M.I. (Ed). Topology in Condensed Matter. Springer Series in Solid-State Sciences (2006) Presented at the Dresde (Germany) "Topology in Condensed Matter Physics" colloquium in June 2002
    • (2006) Springer Series in Solid-State Sciences
    • Mosseri, R.1
  • 176
    • 0030582003 scopus 로고    scopus 로고
    • Seven-sphere and the exceptional N = 7 and N = 8 superconformal algebras
    • arXiv:hep-th/9601072
    • Gunaydin M., and Ketov S.V. Seven-sphere and the exceptional N = 7 and N = 8 superconformal algebras. Nuclear Phys. B467 (1996) 215-246. arXiv:hep-th/9601072
    • (1996) Nuclear Phys. , vol.B467 , pp. 215-246
    • Gunaydin, M.1    Ketov, S.V.2
  • 177
    • 33744938966 scopus 로고    scopus 로고
    • On N = 8 attractors
    • arXiv:hep-th/0603247
    • Ferrara S., and Kallosh R. On N = 8 attractors. Phys. Rev. D73 (2006) 125005. arXiv:hep-th/0603247
    • (2006) Phys. Rev. , vol.D73 , pp. 125005
    • Ferrara, S.1    Kallosh, R.2
  • 178
    • 0000919463 scopus 로고    scopus 로고
    • Multiplet structures of BPS solitons
    • arXiv:hep-th/9708109
    • Lu H., Pope C.N., and Stelle K.S. Multiplet structures of BPS solitons. Classical Quantum Gravity 15 (1998) 537-561. arXiv:hep-th/9708109
    • (1998) Classical Quantum Gravity , vol.15 , pp. 537-561
    • Lu, H.1    Pope, C.N.2    Stelle, K.S.3
  • 179
    • 0002266897 scopus 로고
    • On an Algebraic generalization of the quantum mechanical formalism
    • Jordan P., von Neumann J., and Wigner E.P. On an Algebraic generalization of the quantum mechanical formalism. Ann. of Math. 35 (1934) 29-64
    • (1934) Ann. of Math. , vol.35 , pp. 29-64
    • Jordan, P.1    von Neumann, J.2    Wigner, E.P.3
  • 180
    • 0000568653 scopus 로고
    • Beziehungen der E7 und E8 zur Oktavenebene I-II
    • Freudenthal H. Beziehungen der E7 und E8 zur Oktavenebene I-II. Nederl. Akad. Wetensch. Proc. Ser. 57 (1954) 218-230
    • (1954) Nederl. Akad. Wetensch. Proc. Ser. , vol.57 , pp. 218-230
    • Freudenthal, H.1
  • 181
    • 0000697609 scopus 로고
    • The Freudenthal-Springer-Tits construction of exceptional Jordan algebras
    • McCrimmon K. The Freudenthal-Springer-Tits construction of exceptional Jordan algebras. Trans. Am. Math. Soc. 139 (1969) 495-510
    • (1969) Trans. Am. Math. Soc. , vol.139 , pp. 495-510
    • McCrimmon, K.1
  • 182
    • 34250000281 scopus 로고    scopus 로고
    • Jordan algebras, exceptional groups, and Bhargava composition
    • arXiv:math/0411104
    • Krutelevich S. Jordan algebras, exceptional groups, and Bhargava composition. J. Algebra 314 (2007) 924-977. arXiv:math/0411104
    • (2007) J. Algebra , vol.314 , pp. 924-977
    • Krutelevich, S.1
  • 183
    • 33748849086 scopus 로고
    • The Geometry of N = 2 Maxwell-Einstein Supergravity and Jordan Algebras
    • Gunaydin M., Sierra G., and Townsend P.K. The Geometry of N = 2 Maxwell-Einstein Supergravity and Jordan Algebras. Nuclear Phys. B242 (1984) 244
    • (1984) Nuclear Phys. , vol.B242 , pp. 244
    • Gunaydin, M.1    Sierra, G.2    Townsend, P.K.3
  • 184
    • 0001915676 scopus 로고
    • Exceptional supergravity theories and the magic square
    • Gunaydin M., Sierra G., and Townsend P.K. Exceptional supergravity theories and the magic square. Phys. Lett. B133 (1983) 72
    • (1983) Phys. Lett. , vol.B133 , pp. 72
    • Gunaydin, M.1    Sierra, G.2    Townsend, P.K.3
  • 185
    • 26544448288 scopus 로고
    • Gauging the d = 5 Maxwell-Einstein supergravity theories: More on Jordan algebras
    • Gunaydin M., Sierra G., and Townsend P.K. Gauging the d = 5 Maxwell-Einstein supergravity theories: More on Jordan algebras. Nuclear Phys. B253 (1985) 573
    • (1985) Nuclear Phys. , vol.B253 , pp. 573
    • Gunaydin, M.1    Sierra, G.2    Townsend, P.K.3
  • 186
    • 84945797885 scopus 로고
    • Composition algebras and their automorphisms
    • Jacobson N. Composition algebras and their automorphisms. Rend. Circ. Mat. Palermo 7 (1958) 58-80
    • (1958) Rend. Circ. Mat. Palermo , vol.7 , pp. 58-80
    • Jacobson, N.1
  • 187
    • 0001935641 scopus 로고
    • Uber die Komposition der quadratishen Formen von beliebig vielen Variabeln
    • Hurwitz A. Uber die Komposition der quadratishen Formen von beliebig vielen Variabeln. Nachr. Ges. Wiss. Gottingen (1898) 309-316
    • (1898) Nachr. Ges. Wiss. Gottingen , pp. 309-316
    • Hurwitz, A.1
  • 188
    • 0009258973 scopus 로고
    • Über die Multiplikation quanten-mechanischer Grossen
    • Jordan P. Über die Multiplikation quanten-mechanischer Grossen. Zschr. f. Phys. 80 (1933) 285
    • (1933) Zschr. f. Phys. , vol.80 , pp. 285
    • Jordan, P.1
  • 190
    • 24944505915 scopus 로고    scopus 로고
    • Generalized spacetimes defined by cubic forms and the minimal unitary realizations of their quasiconformal groups
    • arXiv:hep-th/0506010
    • Gunaydin M., and Pavlyk O. Generalized spacetimes defined by cubic forms and the minimal unitary realizations of their quasiconformal groups. J. High Energy Phys. JHEP08 (2005) 101. arXiv:hep-th/0506010
    • (2005) J. High Energy Phys. , vol.JHEP08 , pp. 101
    • Gunaydin, M.1    Pavlyk, O.2
  • 192
    • 84941512492 scopus 로고
    • Group of type E7
    • Brown R.B. Group of type E7. Reine Angew. Math. 236 (1969) 79-102
    • (1969) Reine Angew. Math. , vol.236 , pp. 79-102
    • Brown, R.B.1
  • 193
    • 84941393465 scopus 로고
    • Some groups of transformations defined by Jordan algebras
    • Jacobson N. Some groups of transformations defined by Jordan algebras. J. Reine Angew. Math. 207 (1961) 61-85
    • (1961) J. Reine Angew. Math. , vol.207 , pp. 61-85
    • Jacobson, N.1
  • 194
    • 0001836402 scopus 로고
    • Moufang plane and octonionic quantum mechanics
    • Gunaydin M., Piron C., and Ruegg H. Moufang plane and octonionic quantum mechanics. Comm. Math. Phys. 61 (1978) 69-85
    • (1978) Comm. Math. Phys. , vol.61 , pp. 69-85
    • Gunaydin, M.1    Piron, C.2    Ruegg, H.3
  • 195
    • 0342449294 scopus 로고    scopus 로고
    • Counting BPS black holes in toroidal type II string theory
    • arXiv:hep-th/9903163
    • J.M. Maldacena, G.W. Moore, A. Strominger, Counting BPS black holes in toroidal type II string theory. arXiv:hep-th/9903163
    • Maldacena, J.M.1    Moore, G.W.2    Strominger, A.3
  • 196
    • 0037101537 scopus 로고    scopus 로고
    • On a canonical form of a 3 × 3 Herimitian matrix over the ring of integral split octonions
    • Krutelevich S. On a canonical form of a 3 × 3 Herimitian matrix over the ring of integral split octonions. J. Algebra 253 2 (2002) 276-295
    • (2002) J. Algebra , vol.253 , Issue.2 , pp. 276-295
    • Krutelevich, S.1
  • 197
    • 2442457962 scopus 로고    scopus 로고
    • Higher composition laws I: A new view on Gauss composition, and quadratic generalizations
    • Bhargava M. Higher composition laws I: A new view on Gauss composition, and quadratic generalizations. Ann. of Math. 159 1 (2004) 217-250
    • (2004) Ann. of Math. , vol.159 , Issue.1 , pp. 217-250
    • Bhargava, M.1
  • 198
    • 0001073660 scopus 로고    scopus 로고
    • Universality of supersymmetric attractors
    • arXiv:hep-th/9603090
    • Ferrara S., and Kallosh R. Universality of supersymmetric attractors. Phys. Rev. D54 (1996) 1525-1534. arXiv:hep-th/9603090
    • (1996) Phys. Rev. , vol.D54 , pp. 1525-1534
    • Ferrara, S.1    Kallosh, R.2
  • 199
    • 0002119777 scopus 로고    scopus 로고
    • Five dimensional U-duality, black-hole entropy and topological invariants
    • arXiv:hep-th/9705024
    • Andrianopoli L., D'Auria R., and Ferrara S. Five dimensional U-duality, black-hole entropy and topological invariants. Phys. Lett. B411 (1997) 39-45. arXiv:hep-th/9705024
    • (1997) Phys. Lett. , vol.B411 , pp. 39-45
    • Andrianopoli, L.1    D'Auria, R.2    Ferrara, S.3
  • 200
    • 0032116915 scopus 로고    scopus 로고
    • U-duality, attractors and Bekenstein-Hawking entropy in four and five dimensional supergravities
    • Andrianopoli L., D'Auria R., and Ferrara S. U-duality, attractors and Bekenstein-Hawking entropy in four and five dimensional supergravities. Nuclear Phys. Proc. Suppl. 67 (1998) 17-24
    • (1998) Nuclear Phys. Proc. Suppl. , vol.67 , pp. 17-24
    • Andrianopoli, L.1    D'Auria, R.2    Ferrara, S.3
  • 201
    • 61549112601 scopus 로고    scopus 로고
    • The moduli space of three qutrit states
    • arXiv:quant-ph/0306122
    • E. Briand, J. Luque, J. Thibon, F. Verstraete, The moduli space of three qutrit states. arXiv:quant-ph/0306122
    • Briand, E.1    Luque, J.2    Thibon, J.3    Verstraete, F.4
  • 202
    • 35448969391 scopus 로고    scopus 로고
    • N = 8 non-BPS attractors, fixed scalars and magic supergravities
    • arXiv:0705.3866 [hep-th]
    • Ferrara S., and Marrani A. N = 8 non-BPS attractors, fixed scalars and magic supergravities. Nuclear Phys. B788 (2008) 63-88 arXiv:0705.3866 [hep-th]
    • (2008) Nuclear Phys. , vol.B788 , pp. 63-88
    • Ferrara, S.1    Marrani, A.2
  • 203
    • 61549113281 scopus 로고    scopus 로고
    • Jordan algebras and extremal black holes
    • arXiv:hep-th/0703238
    • M. Rios, Jordan algebras and extremal black holes. arXiv:hep-th/0703238
    • Rios, M.1
  • 204
    • 33845742442 scopus 로고    scopus 로고
    • Magic supergravities, N = 8 and black hole composites
    • arXiv:hep-th/0606211
    • Ferrara S., Gimon E.G., and Kallosh R. Magic supergravities, N = 8 and black hole composites. Phys. Rev. D74 (2006) 125018. arXiv:hep-th/0606211
    • (2006) Phys. Rev. , vol.D74 , pp. 125018
    • Ferrara, S.1    Gimon, E.G.2    Kallosh, R.3
  • 207
    • 33645519586 scopus 로고    scopus 로고
    • Entanglement interpretation of black hole entropy in string theory
    • arXiv:hep-th/0508217
    • Brustein R., Einhorn M.B., and Yarom A. Entanglement interpretation of black hole entropy in string theory. J. High Energy Phys. JHEP01 (2006) 098. arXiv:hep-th/0508217
    • (2006) J. High Energy Phys. , vol.JHEP01 , pp. 098
    • Brustein, R.1    Einhorn, M.B.2    Yarom, A.3
  • 208
    • 33745748477 scopus 로고    scopus 로고
    • Black hole entropy as entanglement entropy: A holographic derivation
    • arXiv:hep-th/0603081
    • Emparan R. Black hole entropy as entanglement entropy: A holographic derivation. J. High Energy Phys. JHEP06 (2006) 012. arXiv:hep-th/0603081
    • (2006) J. High Energy Phys. , vol.JHEP06 , pp. 012
    • Emparan, R.1
  • 209
    • 33947677685 scopus 로고    scopus 로고
    • AdS/CFT and strong subadditivity of entanglement entropy
    • arXiv:hep-th/0608213
    • Hirata T., and Takayanagi T. AdS/CFT and strong subadditivity of entanglement entropy. J. High Energy Phys. JHEP02 (2007) 042. arXiv:hep-th/0608213
    • (2007) J. High Energy Phys. , vol.JHEP02 , pp. 042
    • Hirata, T.1    Takayanagi, T.2
  • 210
    • 33748289532 scopus 로고    scopus 로고
    • Aspects of holographic entanglement entropy
    • arXiv:hep-th/0605073
    • Ryu S., and Takayanagi T. Aspects of holographic entanglement entropy. J. High Energy Phys. JHEP08 (2006) 045. arXiv:hep-th/0605073
    • (2006) J. High Energy Phys. , vol.JHEP08 , pp. 045
    • Ryu, S.1    Takayanagi, T.2
  • 211
    • 61549130087 scopus 로고    scopus 로고
    • M. Blasone, F. Dell'Anno, S. De Siena, F. Illuminati, Entropy, entanglement, and transition probabilities in neutrino oscillations. arXiv:0707.4476 [hep-ph]
    • M. Blasone, F. Dell'Anno, S. De Siena, F. Illuminati, Entropy, entanglement, and transition probabilities in neutrino oscillations. arXiv:0707.4476 [hep-ph]
  • 212
    • 43049149435 scopus 로고    scopus 로고
    • Quantum entanglement and teleportation in higher dimensional black hole spacetimes
    • arXiv:0707.4523 [quant-ph]
    • Ge X.-H., and Kim S.P. Quantum entanglement and teleportation in higher dimensional black hole spacetimes. Classical Quantum Gravity 25 (2008) 075011 arXiv:0707.4523 [quant-ph]
    • (2008) Classical Quantum Gravity , vol.25 , pp. 075011
    • Ge, X.-H.1    Kim, S.P.2
  • 213
    • 0032517030 scopus 로고    scopus 로고
    • Horizon geometry, duality and fixed scalars in six dimensions
    • arXiv:hep-th/9802147
    • Andrianopoli L., D'Auria R., Ferrara S., and Lledo M.A. Horizon geometry, duality and fixed scalars in six dimensions. Nuclear Phys. B528 (1998) 218-228. arXiv:hep-th/9802147
    • (1998) Nuclear Phys. , vol.B528 , pp. 218-228
    • Andrianopoli, L.1    D'Auria, R.2    Ferrara, S.3    Lledo, M.A.4
  • 215
    • 0347942331 scopus 로고
    • Über Verallgemeinerungsmöglichkeiten des Formalismus der Quantenmechanik
    • Jordan P. Über Verallgemeinerungsmöglichkeiten des Formalismus der Quantenmechanik. Nachr. Ges. Wiss. Gottingen (1933) 209-214
    • (1933) Nachr. Ges. Wiss. Gottingen , pp. 209-214
    • Jordan, P.1
  • 216
    • 5644293134 scopus 로고    scopus 로고
    • Foundations of quantum mechanics: Building on von Neumann's heritage
    • Emch G.G. Foundations of quantum mechanics: Building on von Neumann's heritage. Int. J. Quantum. Chem. 65 5 (1997) 379-387
    • (1997) Int. J. Quantum. Chem. , vol.65 , Issue.5 , pp. 379-387
    • Emch, G.G.1
  • 217
    • 61549131526 scopus 로고    scopus 로고
    • On a Jordan algebraic formulation of quantum mechanics: Hilbert space construction
    • arXiv:hep-th/9304124
    • W. Bischoff, On a Jordan algebraic formulation of quantum mechanics: Hilbert space construction. arXiv:hep-th/9304124
    • Bischoff, W.1
  • 219
    • 0030364667 scopus 로고    scopus 로고
    • Octonionic quantum mechanics and complex geometry
    • arXiv:hep-th/9609032
    • De Leo S., and Abdel-Khalek K. Octonionic quantum mechanics and complex geometry. Progr. Theoret. Phys. 96 (1996) 823-832. arXiv:hep-th/9609032
    • (1996) Progr. Theoret. Phys. , vol.96 , pp. 823-832
    • De Leo, S.1    Abdel-Khalek, K.2
  • 220
    • 21144479292 scopus 로고
    • Finite Lorentz transformations, automorphisms, and division algebras
    • arXiv:hep-th/9302044
    • Manogue C.A., and Schray J. Finite Lorentz transformations, automorphisms, and division algebras. J. Math. Phys. 34 (1993) 3746-3767. arXiv:hep-th/9302044
    • (1993) J. Math. Phys. , vol.34 , pp. 3746-3767
    • Manogue, C.A.1    Schray, J.2
  • 221
    • 33746328335 scopus 로고    scopus 로고
    • Is quantum mechanics an island in theoryspace?
    • arXiv:quant-ph/0401062
    • S. Aaronson, Is quantum mechanics an island in theoryspace? arXiv:quant-ph/0401062
    • Aaronson, S.1
  • 223
    • 0030569228 scopus 로고    scopus 로고
    • Overlapping branes in M-theory
    • arXiv:hep-th/9604179
    • Gauntlett J.P., Kastor D.A., and Traschen J.H. Overlapping branes in M-theory. Nuclear Phys. B478 (1996) 544-560. arXiv:hep-th/9604179
    • (1996) Nuclear Phys. , vol.B478 , pp. 544-560
    • Gauntlett, J.P.1    Kastor, D.A.2    Traschen, J.H.3
  • 224
    • 0004249814 scopus 로고    scopus 로고
    • Intersecting branes
    • arXiv:hep-th/9705011
    • J.P. Gauntlett, Intersecting branes. arXiv:hep-th/9705011
    • Gauntlett, J.P.1
  • 225
    • 0030576751 scopus 로고    scopus 로고
    • Harmonic superpositions of M-branes
    • arXiv:hep-th/9604035
    • Tseytlin A.A. Harmonic superpositions of M-branes. Nuclear Phys. B475 (1996) 149-163. arXiv:hep-th/9604035
    • (1996) Nuclear Phys. , vol.B475 , pp. 149-163
    • Tseytlin, A.A.1
  • 226
    • 0030576771 scopus 로고    scopus 로고
    • Intersecting M-branes as four-dimensional black holes
    • arXiv:hep-th/9604166
    • Klebanov I.R., and Tseytlin A.A. Intersecting M-branes as four-dimensional black holes. Nuclear Phys. B475 (1996) 179-192. arXiv:hep-th/9604166
    • (1996) Nuclear Phys. , vol.B475 , pp. 179-192
    • Klebanov, I.R.1    Tseytlin, A.A.2
  • 227
    • 0004342848 scopus 로고    scopus 로고
    • How to count the states of extremal black holes in N = 8 supergravity
    • arXiv:hep-th/9712215
    • V. Balasubramanian, How to count the states of extremal black holes in N = 8 supergravity. arXiv:hep-th/9712215
    • Balasubramanian, V.1
  • 228
    • 0034726187 scopus 로고    scopus 로고
    • Regular BPS black holes: Macroscopic and microscopic description of the generating solution
    • arXiv:hep-th/0002191
    • Bertolini M., and Trigiante M. Regular BPS black holes: Macroscopic and microscopic description of the generating solution. Nuclear Phys. B582 (2000) 393-406. arXiv:hep-th/0002191
    • (2000) Nuclear Phys. , vol.B582 , pp. 393-406
    • Bertolini, M.1    Trigiante, M.2
  • 229
    • 6444241921 scopus 로고    scopus 로고
    • Microscopic entropy of the most general four-dimensional BPS black hole
    • arXiv:hep-th/0008201
    • Bertolini M., and Trigiante M. Microscopic entropy of the most general four-dimensional BPS black hole. J. High Energy Phys. JHEP10 (2000) 002. arXiv:hep-th/0008201
    • (2000) J. High Energy Phys. , vol.JHEP10 , pp. 002
    • Bertolini, M.1    Trigiante, M.2
  • 230
    • 0001085464 scopus 로고    scopus 로고
    • Intersecting M-branes
    • arXiv:hep-th/9603087
    • Papadopoulos G., and Townsend P.K. Intersecting M-branes. Phys. Lett. B380 (1996) 273-279. arXiv:hep-th/9603087
    • (1996) Phys. Lett. , vol.B380 , pp. 273-279
    • Papadopoulos, G.1    Townsend, P.K.2
  • 231
    • 33644751632 scopus 로고    scopus 로고
    • New connections between 4D and 5D black holes
    • arXiv:hep-th/0503217
    • Gaiotto D., Strominger A., and Yin X. New connections between 4D and 5D black holes. J. High Energy Phys. JHEP02 (2006) 024. arXiv:hep-th/0503217
    • (2006) J. High Energy Phys. , vol.JHEP02 , pp. 024
    • Gaiotto, D.1    Strominger, A.2    Yin, X.3
  • 232
    • 33644759226 scopus 로고    scopus 로고
    • 5D black rings and 4D black holes
    • arXiv:hep-th/0504126
    • Gaiotto D., Strominger A., and Yin X. 5D black rings and 4D black holes. J. High Energy Phys. JHEP02 (2006) 023. arXiv:hep-th/0504126
    • (2006) J. High Energy Phys. , vol.JHEP02 , pp. 023
    • Gaiotto, D.1    Strominger, A.2    Yin, X.3
  • 233
    • 61549111989 scopus 로고    scopus 로고
    • The polynomial invariants of four qubits
    • arXiv:quant-ph/0212069
    • J.-G. Luque, J.-Y. Thibon, The polynomial invariants of four qubits. arXiv:quant-ph/0212069
    • Luque, J.-G.1    Thibon, J.-Y.2
  • 234
    • 33748945051 scopus 로고    scopus 로고
    • Hidden symmetries of the Nambu-Goto action
    • arXiv:hep-th/0602160
    • Duff M.J. Hidden symmetries of the Nambu-Goto action. Phys. Lett. B641 (2006) 335-337. arXiv:hep-th/0602160
    • (2006) Phys. Lett. , vol.B641 , pp. 335-337
    • Duff, M.J.1
  • 235
    • 34547652891 scopus 로고    scopus 로고
    • Green-Schwarz, Nambu-Goto actions, and Cayley's hyperdeterminant
    • arXiv:0709.0973 [hep-th]
    • Nishino H., and Rajpoot S. Green-Schwarz, Nambu-Goto actions, and Cayley's hyperdeterminant. Phys. Lett. B652 (2007) 135-140 arXiv:0709.0973 [hep-th]
    • (2007) Phys. Lett. , vol.B652 , pp. 135-140
    • Nishino, H.1    Rajpoot, S.2
  • 237
    • 33846177619 scopus 로고    scopus 로고
    • A complete set of covariants of the four qubit system
    • arXiv:quant-ph/0304026
    • E. Briand, J.G. Luque, J.Y. Thibon, A complete set of covariants of the four qubit system. arXiv:quant-ph/0304026
    • Briand, E.1    Luque, J.G.2    Thibon, J.Y.3
  • 238
    • 61549089151 scopus 로고    scopus 로고
    • Polynomial invariants and bell inequalities as entanglement measure of 4-qubit states
    • arXiv:quant-ph/0606215
    • J. Endrejat, H. Buettner, Polynomial invariants and bell inequalities as entanglement measure of 4-qubit states. arXiv:quant-ph/0606215
    • Endrejat, J.1    Buettner, H.2
  • 241
    • 37649009662 scopus 로고    scopus 로고
    • Simple finite non-abelian flavor groups
    • arXiv:0709.1447 [hep-th]
    • Luhn C., Nasri S., and Ramond P. Simple finite non-abelian flavor groups. J. Math. Phys. 48 (2007) 123519 arXiv:0709.1447 [hep-th]
    • (2007) J. Math. Phys. , vol.48 , pp. 123519
    • Luhn, C.1    Nasri, S.2    Ramond, P.3
  • 242
    • 49749134286 scopus 로고    scopus 로고
    • Anomaly conditions for non-abelian finite family symmetries
    • arXiv:0805.1736 [hep-ph]
    • Luhn C., and Ramond P. Anomaly conditions for non-abelian finite family symmetries. J. High Energy Phys. JHEP07 (2008) 085 arXiv:0805.1736 [hep-ph]
    • (2008) J. High Energy Phys. , vol.JHEP07 , pp. 085
    • Luhn, C.1    Ramond, P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.