메뉴 건너뛰기




Volumn 32, Issue 11, 2002, Pages 1671-1699

The hyperbolic geometric structure of the density matrix for mixed state qubits

Author keywords

Gyrogroup and gyrovector space theory; Hyperbolic geometry; Quantum computation geometry; Special relativity

Indexed keywords


EID: 0036962397     PISSN: 00159018     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021446605657     Document Type: Article
Times cited : (15)

References (50)
  • 3
    • 0001295223 scopus 로고    scopus 로고
    • Quantum entropy and special relativity
    • A. Peres, P. F. Scudo, and D. R. Terno, "Quantum entropy and special relativity," Phys. Rev. Lett. 88, 230402 (2002).
    • (2002) Phys. Rev. Lett. , vol.88 , pp. 230402
    • Peres, A.1    Scudo, P.F.2    Terno, D.R.3
  • 4
    • 0002461583 scopus 로고
    • Thomas rotation and the parametrization of the Lorentz transformation group
    • A. A. Ungar, "Thomas rotation and the parametrization of the Lorentz transformation group," Found. Phys. Lett. 1, 57-89 (1988).
    • (1988) Found. Phys. Lett. , vol.1 , pp. 57-89
    • Ungar, A.A.1
  • 5
    • 0004276578 scopus 로고    scopus 로고
    • Springer, New York
    • R. U. Sexl and H. K. Urbantke, Relativity, Groups, Particles (Springer, New York, 2001). (Special relativity and relativistic symmetry in field and particle physics, Revised and translated from the third German (1992) edition by Urbantke.)
    • (2001) Relativity, Groups, Particles
    • Sexl, R.U.1    Urbantke, H.K.2
  • 6
    • 0038772222 scopus 로고    scopus 로고
    • On the appeal to a pre-established harmony between pure mathematics and relativity physics
    • A. A. Ungar, "On the appeal to a pre-established harmony between pure mathematics and relativity physics," Found. Phys. 33, 2003.
    • (2003) Found. Phys. , vol.33
    • Ungar, A.A.1
  • 7
    • 0001765475 scopus 로고
    • Relativity in late Wilhelmian Germany: The appeal to a preestablished harmony between mathematics and physics
    • L. Pyenson, "Relativity in late Wilhelmian Germany: The appeal to a preestablished harmony between mathematics and physics," Arch. Hist. Exact Sci. 27(2), 137-155 (1982).
    • (1982) Arch. Hist. Exact Sci. , vol.27 , Issue.2 , pp. 137-155
    • Pyenson, L.1
  • 8
    • 0002588888 scopus 로고
    • The expanding Minkowski space
    • A. A. Ungar, "The expanding Minkowski space," Resultate Math. 17(3/4), 342-354 (1990).
    • (1990) Resultate Math. , vol.17 , Issue.3-4 , pp. 342-354
    • Ungar, A.A.1
  • 9
    • 0042025795 scopus 로고
    • Comment on: 'the expanding Minkowski space', [resultate math. 17(3/4), 342-354 (1990), MR 92d:83005] by A. A. Ungar
    • H. Urbantke, "Comment on: 'The expanding Minkowski space', [Resultate Math. 17(3/4), 342-354 (1990), MR 92d:83005] by A. A. Ungar," Results Math. 19(1/2), 189-191 (1991).
    • (1991) Results Math. , vol.19 , Issue.1-2 , pp. 189-191
    • Urbantke, H.1
  • 10
    • 0036409348 scopus 로고    scopus 로고
    • Introducing the Einstein metric to quantum computation and quantum information geometry
    • J.-L. Chen and A. A. Ungar, "Introducing the Einstein metric to quantum computation and quantum information geometry," Found. Phys. Lett. 15(2), 189-197 (2002).
    • (2002) Found. Phys. Lett. , vol.15 , Issue.2 , pp. 189-197
    • Chen, J.-L.1    Ungar, A.A.2
  • 11
    • 0036295343 scopus 로고    scopus 로고
    • The bloch gyrovector
    • J.-L. Chen and A. A. Ungar, "The Bloch gyrovector," Found. Phys. 32(4), 531-565 (2002).
    • (2002) Found. Phys. , vol.32 , Issue.4 , pp. 531-565
    • Chen, J.-L.1    Ungar, A.A.2
  • 12
    • 0036474379 scopus 로고    scopus 로고
    • Geometric observation of Bures fidelity between two states of a qubit
    • J.-L. Chen, L. Fu, A. A. Ungar, and X.-G. Zhao, "Geometric observation of Bures fidelity between two states of a qubit," Phys. Rev. A (3) 65(2), 024303, 3 (2002).
    • (2002) Phys. Rev. A (3) , vol.65 , Issue.2 , pp. 24303
    • Chen, J.-L.1    Fu, L.2    Ungar, A.A.3    Zhao, X.-G.4
  • 13
    • 84976651235 scopus 로고
    • Zur elektrodynamik bewegter körper
    • A. Einstein, "Zur Elektrodynamik Bewegter Körper [On the electrodynamics of moving bodies]," Ann. Phys. (Leipzig) 17, 891-921 (1905).
    • (1905) Ann. Phys. (Leipzig) , vol.17 , pp. 891-921
    • Einstein, A.1
  • 14
    • 0003594793 scopus 로고
    • Dover, New York
    • H. A. Lorentz, A. Einstein, H. Minkowski, and H. Weyl, The Principle of Relativity (Dover, New York, 1952). With notes by A. Sommerfeld, translated by W. Perrett and G. B. Jeffery; a collection of original memoirs on the special and general theory of relativity.
    • (1952) The Principle of Relativity
    • Lorentz, H.A.1    Einstein, A.2    Minkowski, H.3    Weyl, H.4
  • 15
    • 0003408049 scopus 로고    scopus 로고
    • Princeton University Press, Princeton
    • A. Einstein, Einstein's Miraculous Years: Five Papers that Changed the Face of Physics (Princeton University Press, Princeton, 1998). Edited and introduced by John Stachel. [Includes bibliographical references, Einstein's dissertation on the determination of molecular dimensions, Einstein on Brownian motion, Einstein on the theory of relativity, Einstein's early work on the quantum hypothesis, and a new English translation of Einstein's 1905.]
    • (1998) Einstein's Miraculous Years: Five Papers That Changed the Face of Physics
    • Einstein, A.1
  • 17
    • 0042025805 scopus 로고
    • Beiträge zur nichteuklidischen geometrie
    • V. Varičak, "Beiträge zur nichteuklidischen geometrie [contributions to non-Euclidean geometry]." Jber. Dtsch. Mat. Ver. 17, 70-83 (1908).
    • (1908) Jber. Dtsch. Mat. Ver. , vol.17 , pp. 70-83
    • Varičak, V.1
  • 18
    • 0041524790 scopus 로고
    • Anwendung der lobatschefskjschen geometrie in der relativtheorie
    • V. Varičak, "Anwendung der Lobatschefskjschen Geometrie in der Relativtheorie," Phys. Z. 11, 93-96 (1910).
    • (1910) Phys. Z. , vol.11 , pp. 93-96
    • Varičak, V.1
  • 19
    • 0041524792 scopus 로고
    • Über die nichteuklidische interpretation der rela-tivit atstheorie
    • V. Varičak, Über die Nichteuklidische interpretation der Rela-tivit atstheorie [On the non-Euclidean interpretation of relativity theory]," Jber. Dtsch. Mat. Ver. 21, 103-127 (1912).
    • (1912) Jber. Dtsch. Mat. Ver. , vol.21 , pp. 103-127
    • Varičak, V.1
  • 20
    • 0009097672 scopus 로고
    • Springer, New York
    • B. A. Rosenfeld, A History of Non-Euclidean Geometry (Springer, New York, 1988). Evolution of the concept of a geometric space, translated from the Russian by Abe Shenitzer.
    • (1988) A History of Non-Euclidean Geometry
    • Rosenfeld, B.A.1
  • 21
    • 0004188454 scopus 로고
    • Pergamon Press, New York
    • W. Pauli, Theory of Relativity (Pergamon Press, New York, 1958). Translated from the German by G. Field, with supplementary notes by the author.
    • (1958) Theory of Relativity
    • Pauli, W.1
  • 22
    • 0042025724 scopus 로고    scopus 로고
    • The non-Euclidean style of Minkowskian relativity
    • Jeremy J. Gray, ed. Oxford University Press, Oxford
    • S. Walter, "The non-Euclidean style of Minkowskian relativity," in The Symbolic Universe, Jeremy J. Gray, ed. (Oxford University Press, Oxford, 1999), pp. 91-127.
    • (1999) The Symbolic Universe , pp. 91-127
    • Walter, S.1
  • 26
    • 0034388513 scopus 로고    scopus 로고
    • Involutory decomposition of groups into twisted subgroups and subgroups
    • T. Foguel and A. A. Ungar, "Involutory decomposition of groups into twisted subgroups and subgroups," J. Group Theory 3(1), 27-46 (2000).
    • (2000) J. Group Theory , vol.3 , Issue.1 , pp. 27-46
    • Foguel, T.1    Ungar, A.A.2
  • 27
    • 0002984206 scopus 로고    scopus 로고
    • Gyrogroups and the decomposition of groups into twisted subgroups and subgroups
    • T. Foguel and A. A. Ungar, "Gyrogroups and the decomposition of groups into twisted subgroups and subgroups," Pac. J. Math. 197(1), 1-11 (2001).
    • (2001) Pac. J. Math. , vol.197 , Issue.1 , pp. 1-11
    • Foguel, T.1    Ungar, A.A.2
  • 28
    • 0041524785 scopus 로고    scopus 로고
    • The gyro-structure of the complex unit disk
    • M. K. Kinyon and A. A. Ungar, "The gyro-structure of the complex unit disk," Math. Mag. 73(4), 273-284 (2000).
    • (2000) Math. Mag. , vol.73 , Issue.4 , pp. 273-284
    • Kinyon, M.K.1    Ungar, A.A.2
  • 29
    • 23044527469 scopus 로고    scopus 로고
    • Nonassociative geometry of special relativity
    • L. Sbitneva, "Nonassociative geometry of special relativity," Internat. J. Theoret. Phys. 40(1), 359-362 (2001).
    • (2001) Internat. J. Theoret. Phys. , vol.40 , Issue.1 , pp. 359-362
    • Sbitneva, L.1
  • 32
    • 0030587380 scopus 로고    scopus 로고
    • Extension of the unit disk gyrogroup into the unit ball of any real inner product space
    • A. A. Ungar, "Extension of the unit disk gyrogroup into the unit ball of any real inner product space," J. Math. Anal. Appl. 202(3), 1040-1057 (1996).
    • (1996) J. Math. Anal. Appl. , vol.202 , Issue.3 , pp. 1040-1057
    • Ungar, A.A.1
  • 33
    • 0035255818 scopus 로고    scopus 로고
    • The hyperbolic derivative in the Poincaré ball model of hyperbolic geometry
    • G. S. Birman and A. A. Ungar, "The hyperbolic derivative in the Poincaré ball model of hyperbolic geometry," J. Math. Anal. Appl. 254, 321-333 (2001).
    • (2001) J. Math. Anal. Appl. , vol.254 , pp. 321-333
    • Birman, G.S.1    Ungar, A.A.2
  • 34
    • 0033240395 scopus 로고    scopus 로고
    • The hyperbolic Pythagorean theorem in the Poincaré disc model of hyperbolic geometry
    • A. A. Ungar, "The hyperbolic Pythagorean theorem in the Poincaré disc model of hyperbolic geometry," Amer. Math. Monthly 106(8), 759-763 (1999).
    • (1999) Amer. Math. Monthly , vol.106 , Issue.8 , pp. 759-763
    • Ungar, A.A.1
  • 35
    • 0032344813 scopus 로고    scopus 로고
    • From Pythagoras to Einstein: The hyperbolic Pythagorean theorem
    • A. A. Ungar, "From Pythagoras to Einstein: the hyperbolic Pythagorean theorem," Found. Phys. 28(8), 1283-1321 (1998).
    • (1998) Found. Phys. , vol.28 , Issue.8 , pp. 1283-1321
    • Ungar, A.A.1
  • 36
  • 37
    • 0036577976 scopus 로고    scopus 로고
    • Alternative fidelity measure between two states of an n-state quantum system
    • J.-L. Chen, L. Fu, A. A. Ungar, and X.-G. Zhao, "Alternative fidelity measure between two states of an n-state quantum system," Phys. Rev. A (3) 65, 054303, 3 (2002).
    • (2002) Phys. Rev. A (3) , vol.65 , pp. 54303
    • Chen, J.-L.1    Fu, L.2    Ungar, A.A.3    Zhao, X.-G.4
  • 38
    • 0041524784 scopus 로고    scopus 로고
    • Optimization of coherent attacks in generalizations of the bb84 quantum bit commitment protocol
    • R.W. Spekkens and T. Rudolph, "Optimization of coherent attacks in generalizations of the bb84 quantum bit commitment protocol," Quantum Inf. Comp. 2(1), 66-96 (2002).
    • (2002) Quantum Inf. Comp. , vol.2 , Issue.1 , pp. 66-96
    • Spekkens, R.W.1    Rudolph, T.2
  • 40
    • 0011621908 scopus 로고
    • On generalized cocycle equations
    • B. R. Ebanks and C. T. Ng, "On generalized cocycle equations," Aequationes Math. 46(1/2), 76-90 (1993).
    • (1993) Aequationes Math. , vol.46 , Issue.1-2 , pp. 76-90
    • Ebanks, B.R.1    Ng, C.T.2
  • 41
    • 17444443065 scopus 로고    scopus 로고
    • On central extensions of gyrocommutative gyrogroups
    • K. Rozga, "On central extensions of gyrocommutative gyrogroups," Pacific J. Math. 193(1), 201-218 (2000).
    • (2000) Pacific J. Math. , vol.193 , Issue.1 , pp. 201-218
    • Rozga, K.1
  • 42
    • 0002089006 scopus 로고
    • Weakly associative groups
    • A. A. Ungar, "Weakly associative groups," Resultate Math. 17(1/2), 149-168 (1990).
    • (1990) Resultate Math. , vol.17 , Issue.1-2 , pp. 149-168
    • Ungar, A.A.1
  • 43
    • 0001321336 scopus 로고
    • Thomas precession and its associated grouplike structure
    • A. A. Ungar, "Thomas precession and its associated grouplike structure," Amer. J. Phys. 59(9), 824-834 (1991).
    • (1991) Amer. J. Phys. , vol.59 , Issue.9 , pp. 824-834
    • Ungar, A.A.1
  • 44
    • 0031515045 scopus 로고    scopus 로고
    • Thomas precession: Its underlying gyrogroup axioms and their use in hyperbolic geometry and relativistic physics
    • A. A. Ungar, "Thomas precession: Its underlying gyrogroup axioms and their use in hyperbolic geometry and relativistic physics," Found. Phys. 27(6), 881-951 (1997).
    • (1997) Found. Phys. , vol.27 , Issue.6 , pp. 881-951
    • Ungar, A.A.1
  • 45
    • 84967584135 scopus 로고    scopus 로고
    • K-loops, gyrogroups and symmetric spaces
    • W. Krammer and H. K. Urbantke, "K-loops, gyrogroups and symmetric spaces," Results Math. 33(3/4), 310-327 (1998).
    • (1998) Results Math. , vol.33 , Issue.3-4 , pp. 310-327
    • Krammer, W.1    Urbantke, H.K.2
  • 46
    • 0035529463 scopus 로고    scopus 로고
    • Around the finite-dimensional spectral theorem
    • A. Korányi, "Around the finite-dimensional spectral theorem," Amer. Math. Monthly 108(2), 120-125 (2001).
    • (2001) Amer. Math. Monthly , vol.108 , Issue.2 , pp. 120-125
    • Korányi, A.1
  • 47
    • 0032540147 scopus 로고    scopus 로고
    • Fidelity for displaced squeezed thermal states and the oscillator semigroup
    • H. Scutaru, "Fidelity for displaced squeezed thermal states and the oscillator semigroup," J. Phys. A 31(15), 3659-3663 (1998).
    • (1998) J. Phys. A , vol.31 , Issue.15 , pp. 3659-3663
    • Scutaru, H.1
  • 48
    • 51349163744 scopus 로고
    • Fidelity for mixed quantum states
    • Richard Jozsa, "Fidelity for mixed quantum states," J. Modern Opt. 41(12), 2315-2323 (1994).
    • (1994) J. Modern Opt. , vol.41 , Issue.12 , pp. 2315-2323
    • Jozsa, R.1
  • 50
    • 0034694427 scopus 로고    scopus 로고
    • Geometric quantum computation
    • Artur Ekert, Marie Ericsson, Patrick Hayden, Hitoshi Inamori, Jonathan A. Jones, Daniel K. L. Oi, and Vlatko Vedral, "Geometric quantum computation," J. Modern Opt. 47(14/15), 2501-2513 (2000). Seminar on Fundamentals of Quantum Optics, V (Kühtai, 2000).
    • (2000) J. Modern Opt. , vol.47 , Issue.14-15 , pp. 2501-2513
    • Ekert, A.1    Ericsson, M.2    Hayden, P.3    Inamori, H.4    Jones, J.A.5    Oi, D.K.L.6    Vedral, V.7


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.