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Volumn 36, Issue 11, 2006, Pages 1662-1680

A survey of finite algebraic geometrical structures underlying mutually unbiased quantum measurements

Author keywords

D dimensional Hilbert space; Galois fields and rings; Maximally entangled states; Mutually unbiased bases

Indexed keywords


EID: 33751535753     PISSN: 00159018     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10701-006-9079-3     Document Type: Article
Times cited : (53)

References (53)
  • 1
    • 33751541438 scopus 로고    scopus 로고
    • Quiprocone website, http://www.imaph.tu-bs.de/qi/problems
  • 3
    • 84939349092 scopus 로고
    • Complex sequences with low periodic correlations
    • W O. Alltop, "Complex sequences with low periodic correlations," IEEE Trans. Inf. Theory 26, 350 (1980).
    • (1980) IEEE Trans. Inf. Theory , vol.26 , pp. 350
    • Alltop, W.O.1
  • 4
    • 36149039233 scopus 로고
    • Geometrical description of quantal state determination
    • I. D. Ivanović, "Geometrical description of quantal state determination," J. Phys. A 14, 3241 (1981).
    • (1981) J. Phys. A , vol.14 , pp. 3241
    • Ivanović, I.D.1
  • 5
    • 0004586188 scopus 로고
    • Optimal state-determination by mutually unbiased measurements
    • W. K. Wootters and B. D. Fields, "Optimal state-determination by mutually unbiased measurements," Ann. Phys. (NY) 191, 363 (1989).
    • (1989) Ann. Phys. (NY) , vol.191 , pp. 363
    • Wootters, W.K.1    Fields, B.D.2
  • 6
    • 17044411293 scopus 로고    scopus 로고
    • There is no generalization of known formulas for MUBs
    • C. Archer, "There is no generalization of known formulas for MUBs," J. Math. Phys. 46, 022106 (2005).
    • (2005) J. Math. Phys. , vol.46 , pp. 022106
    • Archer, C.1
  • 8
    • 33751526073 scopus 로고    scopus 로고
    • New construction of MUBs in square dimensions
    • P. Wocjan and T. Beth, "New construction of MUBs in square dimensions," Quant. Inf. Comput. 5, 181 (2005).
    • (2005) Quant. Inf. Comput. , vol.5 , pp. 181
    • Wocjan, P.1    Beth, T.2
  • 10
    • 33745186031 scopus 로고    scopus 로고
    • Quantum measurements and finite geometries
    • W .K. Wootters, "Quantum measurements and finite geometries," Found. Phys. 36, 112 (2006).
    • (2006) Found. Phys. , vol.36 , pp. 112
    • Wootters, W.K.1
  • 12
    • 0042732631 scopus 로고    scopus 로고
    • Single-photon interference in sidebands of phase-modulated light for MUBs
    • J. M. Merolla, Y. Mazurenko, J. P. Goedgebuer, and W. T. Rhodes, "Single-photon interference in sidebands of phase-modulated light for MUBs," Phys. Rev. Lett. 82, 1656 (1999).
    • (1999) Phys. Rev. Lett. , vol.82 , pp. 1656
    • Merolla, J.M.1    Mazurenko, Y.2    Goedgebuer, J.P.3    Rhodes, W.T.4
  • 14
    • 0037171183 scopus 로고    scopus 로고
    • Security of quantum key distribution using d-level systems
    • N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, "Security of quantum key distribution using d-level systems," Phys. Rev. Lett. 88, 127902 (2002).
    • (2002) Phys. Rev. Lett. , vol.88 , pp. 127902
    • Cerf, N.J.1    Bourennane, M.2    Karlsson, A.3    Gisin, N.4
  • 15
    • 84862360666 scopus 로고    scopus 로고
    • Security of quantum key distribution with entangled qudits
    • T. Durt, D. Kaszlikowski, J. L. Chen, and L. C. Kwek, "Security of quantum key distribution with entangled qudits," Phys. Rev. A 69, 032313 (2004).
    • (2004) Phys. Rev. A , vol.69 , pp. 032313
    • Durt, T.1    Kaszlikowski, D.2    Chen, J.L.3    Kwek, L.C.4
  • 18
    • 23944456451 scopus 로고    scopus 로고
    • MUBs and the complementarity polytope
    • I. Bengtsson and A. Ericsson, "MUBs and the complementarity polytope," Open Syst. Inf. 12, 107 (2005).
    • (2005) Open Syst. Inf. , vol.12 , pp. 107
    • Bengtsson, I.1    Ericsson, A.2
  • 20
    • 33744516807 scopus 로고    scopus 로고
    • Angular momentum and MUBs
    • M. R. Kibler, "Angular momentum and MUBs," Int. J. Mod. Phys. B 20, 1792 (2006).
    • (2006) Int. J. Mod. Phys. B , vol.20 , pp. 1792
    • Kibler, M.R.1
  • 22
    • 0008001217 scopus 로고    scopus 로고
    • Mixed-state entanglement and distillation: Is there a "bound" entanglement in nature?
    • M. Horodecki, P. Horodecki, and R. Horodecki, "Mixed-state entanglement and distillation: Is there a "bound" entanglement in nature?," Phys. Rev. Lett. 80, 5239 (1998);
    • (1998) Phys. Rev. Lett. , vol.80 , pp. 5239
    • Horodecki, M.1    Horodecki, P.2    Horodecki, R.3
  • 23
    • 33748930819 scopus 로고    scopus 로고
    • The state space for 2 qutrits has a phase space structure in its core
    • B. Baumgartner, B. C. Hiesmayr, and H. Narnhofer, "The state space for 2 qutrits has a phase space structure in its core," Phys. Rev. A. 74, 032327 (2006).
    • (2006) Phys. Rev. A , vol.74 , pp. 032327
    • Baumgartner, B.1    Hiesmayr, B.C.2    Narnhofer, H.3
  • 25
    • 2142709594 scopus 로고    scopus 로고
    • Quantum systems with finite Hilbert space
    • A. Vourdas, "Quantum systems with finite Hilbert space," Rep. Prog. Phys. 67, 267 (2004);
    • (2004) Rep. Prog. Phys. , vol.67 , pp. 267
    • Vourdas, A.1
  • 26
    • 33749503761 scopus 로고    scopus 로고
    • The Frobenius formalism in Galois quantum systems
    • "The Frobenius formalism in Galois quantum systems," Acta Appl. Math. 93, 197 (2006).
    • (2006) Acta Appl. Math. , vol.93 , pp. 197
  • 27
  • 28
    • 26044454623 scopus 로고    scopus 로고
    • Mutually unbiased phase states, phase uncertainties, and Gauss sums
    • "Mutually unbiased phase states, phase uncertainties, and Gauss sums," Eur. Phys. J. D 36, 133 (2005).
    • (2005) Eur. Phys. J. D , vol.36 , pp. 133
  • 33
    • 42749099079 scopus 로고    scopus 로고
    • Discrete phase space based on finite fields
    • K. S. Gibbons, M. J. Hoffman, and W. K. Wootters, "Discrete phase space based on finite fields," Phys. Rev. A 70, 062101 (2004).
    • (2004) Phys. Rev. A , vol.70 , pp. 062101
    • Gibbons, K.S.1    Hoffman, M.J.2    Wootters, W.K.3
  • 34
    • 10044247120 scopus 로고    scopus 로고
    • Geometric approach to digital quantum information
    • C. Rigetti, R. Mosseri, and M. Devoret, "Geometric approach to digital quantum information," Quantum Inf. Process. 3, 351 (2004).
    • (2004) Quantum Inf. Process. , vol.3 , pp. 351
    • Rigetti, C.1    Mosseri, R.2    Devoret, M.3
  • 35
    • 4344590203 scopus 로고    scopus 로고
    • MUBs, generalized spin matrices and separability
    • A. O. Pittenger and M. H. Rubin, "MUBs, generalized spin matrices and separability," Linear Alg. Appl. 390, 255 (2004).
    • (2004) Linear Alg. Appl. , vol.390 , pp. 255
    • Pittenger, A.O.1    Rubin, M.H.2
  • 37
    • 0003892229 scopus 로고    scopus 로고
    • World Scientific, Singapore
    • Z. X. Wan, Quaternary Codes (World Scientific, Singapore, 1997).
    • (1997) Quaternary Codes
    • Wan, Z.X.1
  • 40
    • 0002887410 scopus 로고
    • The nonexistence of certain finite protective planes
    • R. H. Bruck and H. J. Ryser, "The nonexistence of certain finite protective planes," Can. J. Math. 1, 88 (1949).
    • (1949) Can. J. Math. , vol.1 , pp. 88
    • Bruck, R.H.1    Ryser, H.J.2
  • 41
    • 20444488778 scopus 로고    scopus 로고
    • Sets of MUBs as arcs in finite projective planes?
    • M. Saniga and M. Planat, "Sets of MUBs as arcs in finite projective planes ?," Chaos, Solitos Fract. 26, 1267 (2005).
    • (2005) Chaos, Solitos Fract. , vol.26 , pp. 1267
    • Saniga, M.1    Planat, M.2
  • 42
    • 29144482342 scopus 로고    scopus 로고
    • Hjelmslev geometry of MUBs
    • M. Saniga and M. Planat, "Hjelmslev geometry of MUBs," J. Phys. A 39, 435 (2006).
    • (2006) J. Phys. A , vol.39 , pp. 435
    • Saniga, M.1    Planat, M.2
  • 45
    • 84889235307 scopus 로고    scopus 로고
    • Quantum entanglement and projective ring geometry
    • M. Planat, M. Saniga, and M. R. Kibler, "Quantum entanglement and projective ring geometry," SIGMA 2, 066 (2006).
    • (2006) SIGMA , vol.2 , pp. 066
    • Planat, M.1    Saniga, M.2    Kibler, M.R.3
  • 46
    • 4243805132 scopus 로고
    • Remarkable phase oscillations appearing in the lattice dynamics of EPR states
    • D. I. Fivel, "Remarkable phase oscillations appearing in the lattice dynamics of EPR states," Phys. Rev. Lett. 74, 835 (1995).
    • (1995) Phys. Rev. Lett. , vol.74 , pp. 835
    • Fivel, D.I.1
  • 48
    • 0042243471 scopus 로고    scopus 로고
    • Unextendible product bases, uncompletable product bases and bound entanglement
    • D. P. DiVincenzo, T. Mor, P. W. Shor, J. A. Smolin, and B. M. Terhal, "Unextendible product bases, uncompletable product bases and bound entanglement," Commun. Math. Phys. 238, 379 (2003).
    • (2003) Commun. Math. Phys. , vol.238 , pp. 379
    • Divincenzo, D.P.1    Mor, T.2    Shor, P.W.3    Smolin, J.A.4    Terhal, B.M.5
  • 49
    • 0042542909 scopus 로고    scopus 로고
    • Separability criterion and inseparable mixed states with positive partial transposition
    • P. Horodecki, "Separability criterion and inseparable mixed states with positive partial transposition," Phys. Lett. A 232, 333 (1997).
    • (1997) Phys. Lett. A , vol.232 , pp. 333
    • Horodecki, P.1
  • 50
    • 0037471170 scopus 로고    scopus 로고
    • Classifying N-qubit entanglement via Bell's inequalities
    • S. Yu, Z. B. Chen, J. W. Pan, and Y. D. Zhang, "Classifying N-qubit entanglement via Bell's inequalities," Phys. Rev. Lett. 90, 080401 (2003).
    • (2003) Phys. Rev. Lett. , vol.90 , pp. 080401
    • Yu, S.1    Chen, Z.B.2    Pan, J.W.3    Zhang, Y.D.4
  • 51
    • 0000429436 scopus 로고    scopus 로고
    • Multiparticle generalization of entanglement swapping
    • S. Bose, V. Vedral, and P. L. Knight, "Multiparticle generalization of entanglement swapping," Phys. Rev. A 57, 822 (1998).
    • (1998) Phys. Rev. A , vol.57 , pp. 822
    • Bose, S.1    Vedral, V.2    Knight, P.L.3
  • 52
    • 0242297832 scopus 로고    scopus 로고
    • Geometry of the 3-qubit state, entanglement and division algebras
    • B. A. Bernevig and H. D. Chen, "Geometry of the 3-qubit state, entanglement and division algebras," J. Phys. A 36, 8325 (2003).
    • (2003) J. Phys. A , vol.36 , pp. 8325
    • Bernevig, B.A.1    Chen, H.D.2
  • 53
    • 0344165306 scopus 로고    scopus 로고
    • Quantum entanglement and topological entanglement
    • L. H. Kauffman and S. J. Lomonaco, "Quantum entanglement and topological entanglement," New J. Phys. 4, 73.1 (2002).
    • (2002) New J. Phys. , vol.4
    • Kauffman, L.H.1    Lomonaco, S.J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.