Abstract

We examine the physical significance of fidelity as a measure of similarity for Gaussian states by drawing a comparison with its classical counterpart. We find that the relationship between these classical and quantum fidelities is not straightforward, and in general does not seem to provide insight into the physical significance of quantum fidelity. To avoid this ambiguity we propose that the efficacy of quantum information protocols be characterized by determining their transfer function and then calculating the fidelity achievable for a hypothetical pure reference input state.

© 2007 Optical Society of America

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  1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge U. Press, 2000).
  2. R. Jozsa, "Fidelity for mixed quantum states," J. Mod. Opt. 41, 2315-2323 (1994).
    [CrossRef]
  3. A. Uhlmann, "The 'transition probability' in the state space of a*-algebra," Rep. Math. Phys. 9, 273-279 (1976).
    [CrossRef]
  4. S. L. Braunstein, C. A. Fuchs, and H. J. Kimble, "Criteria for continuous-variable quantum teleportation," J. Mod. Opt. 47, 267-278 (2000).
    [CrossRef]
  5. J. L. Dodd and M. A. Nielsen, "Simple operational interpretation of the fidelity of mixed states," Phys. Rev. A 66, 044301 (2002).
    [CrossRef]
  6. J. Lee, M. S. Kim, and C. Brukner, "Operationally invariant measure of the distance between quantum states by complementary measurements," Phys. Rev. Lett. 91, 087902 (2003).
    [CrossRef] [PubMed]
  7. A. Gilchrist, N. K. Langford, and M. A. Nielsen, "Distance measures to compare real and ideal quantum processes," Phys. Rev. A 71, 062310 (2005).
    [CrossRef]
  8. A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
    [CrossRef] [PubMed]
  9. W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, "Experimental investigation of continuous-variable quantum teleportation," Phys. Rev. A 67, 032302 (2003).
    [CrossRef]
  10. W.P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, T. Symul, and P. K. Lam, "Unity gain and nonunity gain quantum teleportation," IEEE J. Sel. Top. Quantum Electron. 9, 1519-1532 (2003).
    [CrossRef]
  11. T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, "Quantum teleportation of light beams," Phys. Rev. A 67, 033802 (2003).
    [CrossRef]
  12. A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, "Tripartite quantum state sharing," Phys. Rev. Lett. 92, 177903 (2004).
    [CrossRef] [PubMed]
  13. F. Grosshans and P. Grangier, "Quantum cloning and teleportation criteria for continuous quantum variables," Phys. Rev. A 64, 010301 (2001).
    [CrossRef]
  14. S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and P. van Loock, "Quantum versus classical domains for teleportation with continuous variables," Phys. Rev. A 64, 022321 (2001).
    [CrossRef]
  15. C. M. Caves and K. Wódkiewicz, "Fidelity of Gaussian channels," Open Syst. Inf. Dyn. 11, 309-323 (2004).
    [CrossRef]
  16. D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, 1994).
  17. H. F. Hofmann, "Complementary classical fidelities as an efficient criterion for the evaluation of experimentally realized quantum operations," Phys. Rev. Lett. 94, 160504 (2005).
    [CrossRef] [PubMed]
  18. J. Lee, M. S. Kim, and H. Jeong, "Transfer of nonclassical features in quantum teleportation via a mixed quantum channel," Phys. Rev. A 62, 032305 (2000).
    [CrossRef]
  19. J. Fiurásek, "Improving fidelity of continuous-variable teleportation via local operations," Phys. Rev. A 66, 012304 (2002).
    [CrossRef]
  20. C. M. Caves and K. Wodkiewicz, "Classical phase-space descriptions of continuous-variable teleportation," http://arxiv.org/abs/quant-ph/0401149 (2004).
  21. J. Twamley, "Bures and statistical distance for squeezed thermal states," J. Phys. A 29, 3723-3731 (1996).
    [CrossRef]
  22. X.-B. Wang, C. H. Oh, and L. C. Kwek, "Bures fidelity of displaced squeezed thermal states," Phys. Rev. A 58, 4186-4190 (1998).
    [CrossRef]
  23. Gh.-S. Paraoanu and H. Scutaru, "Bures distance between two displaced thermal states," Phys. Rev. A 58, 869-871 (1998).
    [CrossRef]
  24. P. Marian, T. A. Marian, and H. Scutaru, "Quantifying nonclassicality of one-mode Gaussian states of the radiation field," Phys. Rev. Lett. 88, 153601 (2002).
    [CrossRef] [PubMed]
  25. There are some exceptions, such as nonunity gain teleportation.
  26. T. C. Ralph and P. K. Lam, "Teleportation with bright squeezed light," Phys. Rev. Lett. 81, 5668-5671 (1998).
    [CrossRef]
  27. This simplifying assumption has no bearing on the conclusions of the analysis.

2005

A. Gilchrist, N. K. Langford, and M. A. Nielsen, "Distance measures to compare real and ideal quantum processes," Phys. Rev. A 71, 062310 (2005).
[CrossRef]

H. F. Hofmann, "Complementary classical fidelities as an efficient criterion for the evaluation of experimentally realized quantum operations," Phys. Rev. Lett. 94, 160504 (2005).
[CrossRef] [PubMed]

2004

A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, "Tripartite quantum state sharing," Phys. Rev. Lett. 92, 177903 (2004).
[CrossRef] [PubMed]

C. M. Caves and K. Wódkiewicz, "Fidelity of Gaussian channels," Open Syst. Inf. Dyn. 11, 309-323 (2004).
[CrossRef]

2003

J. Lee, M. S. Kim, and C. Brukner, "Operationally invariant measure of the distance between quantum states by complementary measurements," Phys. Rev. Lett. 91, 087902 (2003).
[CrossRef] [PubMed]

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, "Experimental investigation of continuous-variable quantum teleportation," Phys. Rev. A 67, 032302 (2003).
[CrossRef]

W.P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, T. Symul, and P. K. Lam, "Unity gain and nonunity gain quantum teleportation," IEEE J. Sel. Top. Quantum Electron. 9, 1519-1532 (2003).
[CrossRef]

T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, "Quantum teleportation of light beams," Phys. Rev. A 67, 033802 (2003).
[CrossRef]

2002

J. L. Dodd and M. A. Nielsen, "Simple operational interpretation of the fidelity of mixed states," Phys. Rev. A 66, 044301 (2002).
[CrossRef]

J. Fiurásek, "Improving fidelity of continuous-variable teleportation via local operations," Phys. Rev. A 66, 012304 (2002).
[CrossRef]

P. Marian, T. A. Marian, and H. Scutaru, "Quantifying nonclassicality of one-mode Gaussian states of the radiation field," Phys. Rev. Lett. 88, 153601 (2002).
[CrossRef] [PubMed]

2001

F. Grosshans and P. Grangier, "Quantum cloning and teleportation criteria for continuous quantum variables," Phys. Rev. A 64, 010301 (2001).
[CrossRef]

S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and P. van Loock, "Quantum versus classical domains for teleportation with continuous variables," Phys. Rev. A 64, 022321 (2001).
[CrossRef]

2000

J. Lee, M. S. Kim, and H. Jeong, "Transfer of nonclassical features in quantum teleportation via a mixed quantum channel," Phys. Rev. A 62, 032305 (2000).
[CrossRef]

S. L. Braunstein, C. A. Fuchs, and H. J. Kimble, "Criteria for continuous-variable quantum teleportation," J. Mod. Opt. 47, 267-278 (2000).
[CrossRef]

1998

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
[CrossRef] [PubMed]

T. C. Ralph and P. K. Lam, "Teleportation with bright squeezed light," Phys. Rev. Lett. 81, 5668-5671 (1998).
[CrossRef]

X.-B. Wang, C. H. Oh, and L. C. Kwek, "Bures fidelity of displaced squeezed thermal states," Phys. Rev. A 58, 4186-4190 (1998).
[CrossRef]

Gh.-S. Paraoanu and H. Scutaru, "Bures distance between two displaced thermal states," Phys. Rev. A 58, 869-871 (1998).
[CrossRef]

1996

J. Twamley, "Bures and statistical distance for squeezed thermal states," J. Phys. A 29, 3723-3731 (1996).
[CrossRef]

1994

R. Jozsa, "Fidelity for mixed quantum states," J. Mod. Opt. 41, 2315-2323 (1994).
[CrossRef]

1976

A. Uhlmann, "The 'transition probability' in the state space of a*-algebra," Rep. Math. Phys. 9, 273-279 (1976).
[CrossRef]

Bachor, H. A.

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, "Experimental investigation of continuous-variable quantum teleportation," Phys. Rev. A 67, 032302 (2003).
[CrossRef]

Bowen, W. P.

A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, "Tripartite quantum state sharing," Phys. Rev. Lett. 92, 177903 (2004).
[CrossRef] [PubMed]

W.P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, T. Symul, and P. K. Lam, "Unity gain and nonunity gain quantum teleportation," IEEE J. Sel. Top. Quantum Electron. 9, 1519-1532 (2003).
[CrossRef]

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, "Experimental investigation of continuous-variable quantum teleportation," Phys. Rev. A 67, 032302 (2003).
[CrossRef]

Braunstein, S. L.

S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and P. van Loock, "Quantum versus classical domains for teleportation with continuous variables," Phys. Rev. A 64, 022321 (2001).
[CrossRef]

S. L. Braunstein, C. A. Fuchs, and H. J. Kimble, "Criteria for continuous-variable quantum teleportation," J. Mod. Opt. 47, 267-278 (2000).
[CrossRef]

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
[CrossRef] [PubMed]

Brukner, C.

J. Lee, M. S. Kim, and C. Brukner, "Operationally invariant measure of the distance between quantum states by complementary measurements," Phys. Rev. Lett. 91, 087902 (2003).
[CrossRef] [PubMed]

Buchler, B. C.

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, "Experimental investigation of continuous-variable quantum teleportation," Phys. Rev. A 67, 032302 (2003).
[CrossRef]

W.P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, T. Symul, and P. K. Lam, "Unity gain and nonunity gain quantum teleportation," IEEE J. Sel. Top. Quantum Electron. 9, 1519-1532 (2003).
[CrossRef]

Caves, C. M.

C. M. Caves and K. Wódkiewicz, "Fidelity of Gaussian channels," Open Syst. Inf. Dyn. 11, 309-323 (2004).
[CrossRef]

C. M. Caves and K. Wodkiewicz, "Classical phase-space descriptions of continuous-variable teleportation," http://arxiv.org/abs/quant-ph/0401149 (2004).

Chou, C. W.

T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, "Quantum teleportation of light beams," Phys. Rev. A 67, 033802 (2003).
[CrossRef]

Chuang, I. L.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge U. Press, 2000).

Dodd, J. L.

J. L. Dodd and M. A. Nielsen, "Simple operational interpretation of the fidelity of mixed states," Phys. Rev. A 66, 044301 (2002).
[CrossRef]

Fiurásek, J.

J. Fiurásek, "Improving fidelity of continuous-variable teleportation via local operations," Phys. Rev. A 66, 012304 (2002).
[CrossRef]

Fuchs, C. A.

S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and P. van Loock, "Quantum versus classical domains for teleportation with continuous variables," Phys. Rev. A 64, 022321 (2001).
[CrossRef]

S. L. Braunstein, C. A. Fuchs, and H. J. Kimble, "Criteria for continuous-variable quantum teleportation," J. Mod. Opt. 47, 267-278 (2000).
[CrossRef]

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
[CrossRef] [PubMed]

Furusawa, A.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
[CrossRef] [PubMed]

Gilchrist, A.

A. Gilchrist, N. K. Langford, and M. A. Nielsen, "Distance measures to compare real and ideal quantum processes," Phys. Rev. A 71, 062310 (2005).
[CrossRef]

Goh, K. W.

T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, "Quantum teleportation of light beams," Phys. Rev. A 67, 033802 (2003).
[CrossRef]

Grangier, P.

F. Grosshans and P. Grangier, "Quantum cloning and teleportation criteria for continuous quantum variables," Phys. Rev. A 64, 010301 (2001).
[CrossRef]

Grosshans, F.

F. Grosshans and P. Grangier, "Quantum cloning and teleportation criteria for continuous quantum variables," Phys. Rev. A 64, 010301 (2001).
[CrossRef]

Hofmann, H. F.

H. F. Hofmann, "Complementary classical fidelities as an efficient criterion for the evaluation of experimentally realized quantum operations," Phys. Rev. Lett. 94, 160504 (2005).
[CrossRef] [PubMed]

Jeong, H.

J. Lee, M. S. Kim, and H. Jeong, "Transfer of nonclassical features in quantum teleportation via a mixed quantum channel," Phys. Rev. A 62, 032305 (2000).
[CrossRef]

Jozsa, R.

R. Jozsa, "Fidelity for mixed quantum states," J. Mod. Opt. 41, 2315-2323 (1994).
[CrossRef]

Kim, M. S.

J. Lee, M. S. Kim, and C. Brukner, "Operationally invariant measure of the distance between quantum states by complementary measurements," Phys. Rev. Lett. 91, 087902 (2003).
[CrossRef] [PubMed]

J. Lee, M. S. Kim, and H. Jeong, "Transfer of nonclassical features in quantum teleportation via a mixed quantum channel," Phys. Rev. A 62, 032305 (2000).
[CrossRef]

Kimble, H. J.

T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, "Quantum teleportation of light beams," Phys. Rev. A 67, 033802 (2003).
[CrossRef]

S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and P. van Loock, "Quantum versus classical domains for teleportation with continuous variables," Phys. Rev. A 64, 022321 (2001).
[CrossRef]

S. L. Braunstein, C. A. Fuchs, and H. J. Kimble, "Criteria for continuous-variable quantum teleportation," J. Mod. Opt. 47, 267-278 (2000).
[CrossRef]

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
[CrossRef] [PubMed]

Kwek, L. C.

X.-B. Wang, C. H. Oh, and L. C. Kwek, "Bures fidelity of displaced squeezed thermal states," Phys. Rev. A 58, 4186-4190 (1998).
[CrossRef]

Lam, P. K.

A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, "Tripartite quantum state sharing," Phys. Rev. Lett. 92, 177903 (2004).
[CrossRef] [PubMed]

W.P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, T. Symul, and P. K. Lam, "Unity gain and nonunity gain quantum teleportation," IEEE J. Sel. Top. Quantum Electron. 9, 1519-1532 (2003).
[CrossRef]

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, "Experimental investigation of continuous-variable quantum teleportation," Phys. Rev. A 67, 032302 (2003).
[CrossRef]

T. C. Ralph and P. K. Lam, "Teleportation with bright squeezed light," Phys. Rev. Lett. 81, 5668-5671 (1998).
[CrossRef]

Lance, A. M.

A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, "Tripartite quantum state sharing," Phys. Rev. Lett. 92, 177903 (2004).
[CrossRef] [PubMed]

Langford, N. K.

A. Gilchrist, N. K. Langford, and M. A. Nielsen, "Distance measures to compare real and ideal quantum processes," Phys. Rev. A 71, 062310 (2005).
[CrossRef]

Lee, J.

J. Lee, M. S. Kim, and C. Brukner, "Operationally invariant measure of the distance between quantum states by complementary measurements," Phys. Rev. Lett. 91, 087902 (2003).
[CrossRef] [PubMed]

J. Lee, M. S. Kim, and H. Jeong, "Transfer of nonclassical features in quantum teleportation via a mixed quantum channel," Phys. Rev. A 62, 032305 (2000).
[CrossRef]

Lodahl, P.

T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, "Quantum teleportation of light beams," Phys. Rev. A 67, 033802 (2003).
[CrossRef]

Marian, P.

P. Marian, T. A. Marian, and H. Scutaru, "Quantifying nonclassicality of one-mode Gaussian states of the radiation field," Phys. Rev. Lett. 88, 153601 (2002).
[CrossRef] [PubMed]

Marian, T. A.

P. Marian, T. A. Marian, and H. Scutaru, "Quantifying nonclassicality of one-mode Gaussian states of the radiation field," Phys. Rev. Lett. 88, 153601 (2002).
[CrossRef] [PubMed]

Milburn, G. J.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, 1994).

Nielsen, M. A.

A. Gilchrist, N. K. Langford, and M. A. Nielsen, "Distance measures to compare real and ideal quantum processes," Phys. Rev. A 71, 062310 (2005).
[CrossRef]

J. L. Dodd and M. A. Nielsen, "Simple operational interpretation of the fidelity of mixed states," Phys. Rev. A 66, 044301 (2002).
[CrossRef]

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge U. Press, 2000).

Oh, C. H.

X.-B. Wang, C. H. Oh, and L. C. Kwek, "Bures fidelity of displaced squeezed thermal states," Phys. Rev. A 58, 4186-4190 (1998).
[CrossRef]

Paraoanu, Gh.-S.

Gh.-S. Paraoanu and H. Scutaru, "Bures distance between two displaced thermal states," Phys. Rev. A 58, 869-871 (1998).
[CrossRef]

Polzik, E. S.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
[CrossRef] [PubMed]

Ralph, T. C.

W.P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, T. Symul, and P. K. Lam, "Unity gain and nonunity gain quantum teleportation," IEEE J. Sel. Top. Quantum Electron. 9, 1519-1532 (2003).
[CrossRef]

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, "Experimental investigation of continuous-variable quantum teleportation," Phys. Rev. A 67, 032302 (2003).
[CrossRef]

T. C. Ralph and P. K. Lam, "Teleportation with bright squeezed light," Phys. Rev. Lett. 81, 5668-5671 (1998).
[CrossRef]

Sanders, B. C.

A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, "Tripartite quantum state sharing," Phys. Rev. Lett. 92, 177903 (2004).
[CrossRef] [PubMed]

Schnabel, R.

W.P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, T. Symul, and P. K. Lam, "Unity gain and nonunity gain quantum teleportation," IEEE J. Sel. Top. Quantum Electron. 9, 1519-1532 (2003).
[CrossRef]

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, "Experimental investigation of continuous-variable quantum teleportation," Phys. Rev. A 67, 032302 (2003).
[CrossRef]

Scutaru, H.

P. Marian, T. A. Marian, and H. Scutaru, "Quantifying nonclassicality of one-mode Gaussian states of the radiation field," Phys. Rev. Lett. 88, 153601 (2002).
[CrossRef] [PubMed]

Gh.-S. Paraoanu and H. Scutaru, "Bures distance between two displaced thermal states," Phys. Rev. A 58, 869-871 (1998).
[CrossRef]

Sørensen, J. L.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
[CrossRef] [PubMed]

Symul, T.

A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, "Tripartite quantum state sharing," Phys. Rev. Lett. 92, 177903 (2004).
[CrossRef] [PubMed]

W.P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, T. Symul, and P. K. Lam, "Unity gain and nonunity gain quantum teleportation," IEEE J. Sel. Top. Quantum Electron. 9, 1519-1532 (2003).
[CrossRef]

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, "Experimental investigation of continuous-variable quantum teleportation," Phys. Rev. A 67, 032302 (2003).
[CrossRef]

Treps, N.

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, "Experimental investigation of continuous-variable quantum teleportation," Phys. Rev. A 67, 032302 (2003).
[CrossRef]

W.P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, T. Symul, and P. K. Lam, "Unity gain and nonunity gain quantum teleportation," IEEE J. Sel. Top. Quantum Electron. 9, 1519-1532 (2003).
[CrossRef]

Twamley, J.

J. Twamley, "Bures and statistical distance for squeezed thermal states," J. Phys. A 29, 3723-3731 (1996).
[CrossRef]

Uhlmann, A.

A. Uhlmann, "The 'transition probability' in the state space of a*-algebra," Rep. Math. Phys. 9, 273-279 (1976).
[CrossRef]

van Loock, P.

S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and P. van Loock, "Quantum versus classical domains for teleportation with continuous variables," Phys. Rev. A 64, 022321 (2001).
[CrossRef]

Walls, D. F.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, 1994).

Wang, X.-B.

X.-B. Wang, C. H. Oh, and L. C. Kwek, "Bures fidelity of displaced squeezed thermal states," Phys. Rev. A 58, 4186-4190 (1998).
[CrossRef]

Wodkiewicz, K.

C. M. Caves and K. Wodkiewicz, "Classical phase-space descriptions of continuous-variable teleportation," http://arxiv.org/abs/quant-ph/0401149 (2004).

Wódkiewicz, K.

C. M. Caves and K. Wódkiewicz, "Fidelity of Gaussian channels," Open Syst. Inf. Dyn. 11, 309-323 (2004).
[CrossRef]

Zhang, T. C.

T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, "Quantum teleportation of light beams," Phys. Rev. A 67, 033802 (2003).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

W.P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, T. Symul, and P. K. Lam, "Unity gain and nonunity gain quantum teleportation," IEEE J. Sel. Top. Quantum Electron. 9, 1519-1532 (2003).
[CrossRef]

J. Mod. Opt.

R. Jozsa, "Fidelity for mixed quantum states," J. Mod. Opt. 41, 2315-2323 (1994).
[CrossRef]

S. L. Braunstein, C. A. Fuchs, and H. J. Kimble, "Criteria for continuous-variable quantum teleportation," J. Mod. Opt. 47, 267-278 (2000).
[CrossRef]

J. Phys. A

J. Twamley, "Bures and statistical distance for squeezed thermal states," J. Phys. A 29, 3723-3731 (1996).
[CrossRef]

Open Syst. Inf. Dyn.

C. M. Caves and K. Wódkiewicz, "Fidelity of Gaussian channels," Open Syst. Inf. Dyn. 11, 309-323 (2004).
[CrossRef]

Phys. Rev. A

J. Lee, M. S. Kim, and H. Jeong, "Transfer of nonclassical features in quantum teleportation via a mixed quantum channel," Phys. Rev. A 62, 032305 (2000).
[CrossRef]

J. Fiurásek, "Improving fidelity of continuous-variable teleportation via local operations," Phys. Rev. A 66, 012304 (2002).
[CrossRef]

T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, "Quantum teleportation of light beams," Phys. Rev. A 67, 033802 (2003).
[CrossRef]

F. Grosshans and P. Grangier, "Quantum cloning and teleportation criteria for continuous quantum variables," Phys. Rev. A 64, 010301 (2001).
[CrossRef]

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This simplifying assumption has no bearing on the conclusions of the analysis.

There are some exceptions, such as nonunity gain teleportation.

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Figures (5)

Fig. 1
Fig. 1

Fidelity limit F ne for quantum teleportation without entanglement against the variance V of an isotropically mixed-state input (solid curve) and the corresponding classical fidelity (dashed curve).

Fig. 2
Fig. 2

Schematic of two arbitrary Gaussian distributions P 1 and P 2 .

Fig. 3
Fig. 3

Quantum (solid curves) and classical (dashed curves) fidelities F between two Gaussian distributions. (a) Both distributions are pure, V 1 + = 2 , V 1 = 1 2 , V 2 + V 2 = 1 , and φ = 0 . (b) One distribution is pure, and the other is mixed but with the same squeezing parameter V 1 + = 2 , V 1 = 1 2 , V 2 + V 2 = 4 , and φ = 0 .

Fig. 4
Fig. 4

Quantum (solid curves) and classical (dashed curves) fidelities between Gaussian distributions. (a) V 1 + = 4 , V 1 = 1 , V 2 + V 2 = 4 , and φ = 0 . (b) V 1 + = 4 , V 1 = 1 , V 2 + V 2 = 4 , and φ = 0 . The breadths of the Gaussian distributions are four times larger than those in Fig. 3.

Fig. 5
Fig. 5

Quantum (solid curve) and classical (dashed curve) fidelities for two Gaussian distributions having the same absolute squeezing parameter V 1 + V 1 = V 2 + V 2 = 16 ( r = 0.693 ) , yet different breadths V 1 + V 1 = V 2 + V 2 4 = 1 . The quantum and classical fidelities vary differently with the relative angle.

Equations (35)

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F ρ 1 , ρ 2 = ψ 1 , 2 max ψ 2 ψ 1 2 ,
ϕ i = 1 G i n [ ( G i 1 ) G i ] n 2 n a n b ,
F = ϕ 1 ϕ 2 2 = 1 G 1 G 2 { n [ ( G 1 1 ) ( G 2 1 ) G 1 G 2 ] n 2 } 2 = [ 1 G 1 G 2 ( G 1 1 ) ( G 2 1 ) ] 2 = [ 2 ( V 1 + 1 ) ( V 2 + 1 ) ( V 1 1 ) ( V 2 1 ) ] 2 ,
F ne = [ 2 ( V + 1 ) ( V + 3 ) ( V 1 ) ( V + 1 ) ] 2 .
F c ( P 1 , P 2 ) = [ d 2 α P 1 ( α ) P 2 ( α ) ] 2 ,
F q ( ρ 1 , ρ 2 ) = { Tr [ ρ 1 ρ 2 ρ 1 ] } 2 ,
W ( α ) = 2 π V + V exp [ 2 V + ( α r cos ϕ + α i sin ϕ δ r ) 2 2 V ( α i cos ϕ α r sin ϕ δ i ) 2 ] ,
r = 1 4 e i ϕ ln [ V V + ] .
α r = α r cos ϕ + α i sin ϕ ,
α i = α i cos ϕ α r sin ϕ ,
F c = 4 V 1 + V 1 V 2 + V 2 { cos 2 φ ( V 1 + + V 2 + ) ( V 1 + V 2 ) + sin 2 φ ( V 1 + + V 2 ) ( V 1 + V 2 + ) } 1 ,
F q = 2 4 V 1 + V 2 + V 1 V 2 F c + K K ,
F c ( φ = 0 ) = 4 V 1 + V 1 V 2 + V 2 ( V 1 + + V 2 + ) ( V 1 + V 2 ) ,
F q ( φ = 0 ) = 2 { ( V 1 + V 2 + 1 ) ( V 1 V 2 + + 1 ) K } 1 .
F c ( V 1 , V 2 ) = 4 V 1 V 2 ( V 1 + V 2 ) 2 ,
F q ( V 1 , V 2 ) = 2 { V 1 V 2 + 1 ( V 1 2 1 ) ( V 2 2 1 ) } 1 ,
F q ( x ) = F q ( φ = 0 ) D ( x ) ,
D ( x ) = exp [ 2 x r 2 V 1 + + V 2 + 2 x 1 2 V 1 + V 2 ] .
F c ( x ) = F c ( φ = 0 ) D ( x ) ,
F q 2 = F c V 2 + V 2 .
V out ± = V in ± + 1 ,
ρ = Z ( β ) D ( x ) S ( r ) exp [ β 2 ( a a + a a ) ] S ( r ) D ( x ) ,
F q ( φ ) = 2 sinh β 1 2 sinh β 2 2 Y 1 ,
Y = cos 2 φ [ cosh 2 ( r 2 r 1 ) cosh 2 ( β 1 + β 2 ) 2 sinh 2 ( r 2 r 1 ) cosh 2 ( β 2 β 1 ) 2 ] + sin φ [ cosh 2 ( r 1 + r 2 ) cosh 2 ( β 1 + β 2 ) 2 sinh 2 ( r 1 + r 2 ) cosh 2 ( β 2 β 1 ) 2 ] .
V + = Δ X 2 = 1 + A + B ,
V = Δ P 2 = 1 + A B ,
A = 2 [ n ¯ + ( 2 n ¯ + 1 ) sinh 2 r ] ,
B = 2 ( 2 n ¯ + 1 ) cosh ϕ sinh r cosh r ,
n ¯ = Tr [ ρ a ̂ a ̂ ] = 1 e β 1 ,
β = ln [ 1 + 2 V + V 1 ] ,
F q ( x ) = F q ( φ = 0 ) D ,
D = exp [ ( ϵ 1 + ϵ 2 ) Δ ] ,
Δ = cos β 1 cosh β 2 + sinh β 1 sinh β 2 cosh 2 ( r 1 r 2 ) 1 ,
ϵ 1 = sinh β 1 sinh 2 β 2 2 [ ( g 2 + g * 2 ) sinh 2 r 1 2 g 2 cosh 2 r 1 ] ,
ϵ 2 = sinh β 2 sinh 2 β 1 2 [ ( g 2 + g * 2 ) sinh 2 r 2 2 g 2 cosh 2 r 2 ] .

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