Fidelity balance in quantum operations

Physical Review Letters

Volumn 86, Issue 7, 2001, Pages 1366-1369

  Banaszek, Konrad ^a  

^a UNIVERSITY OF ROCHESTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BAND STRUCTURE; COMPUTER SIMULATION; ELECTRON ENERGY LEVELS; ELECTRON TRANSITIONS; IONIZATION; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; SPECTRUM ANALYSIS;

COULOMB INTERACTIONS; FIDELITY BALANCE; QUANTUM TELEPORTATION; SCREENING ELECTRONS;

QUANTUM THEORY;

EID: 14344283018     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.86.1366     Document Type: Article

References (19)

1. W. Heisenberg, The Physical Principles of the Quantum Theory (Dover, New York, 1930). Let us note that the Heisenberg uncertainty relation can be assigned two meanings. The first one refers to variances of the position and the momentum when these quantities are determined from disjoint subsets of an ensemble of identically prepared particles. The second meaning, illustrated by the microscope experiment and relevant in the context of information gain versus disturbance, describes a bound on the resolution of an apparatus measuring simultaneously both the conjugate variables. For a detailed discussion, see K. Wódkiewicz, Phys. Lett. A 124, 207 (1987); S. Stenholm, Ann. Phys. (N.Y.) 218, 233 (1992) and references therein.
2. W. Heisenberg, The Physical Principles of the Quantum Theory (Dover, New York, 1930). Let us note that the Heisenberg uncertainty relation can be assigned two meanings. The first one refers to variances of the position and the momentum when these quantities are determined from disjoint subsets of an ensemble of identically prepared particles. The second meaning, illustrated by the microscope experiment and relevant in the context of information gain versus disturbance, describes a bound on the resolution of an apparatus measuring simultaneously both the conjugate variables. For a detailed discussion, see K. Wódkiewicz, Phys. Lett. A 124, 207 (1987); S. Stenholm, Ann. Phys. (N.Y.) 218, 233 (1992) and references therein.
3. W. Heisenberg, The Physical Principles of the Quantum Theory (Dover, New York, 1930). Let us note that the Heisenberg uncertainty relation can be assigned two meanings. The first one refers to variances of the position and the momentum when these quantities are determined from disjoint subsets of an ensemble of identically prepared particles. The second meaning, illustrated by the microscope experiment and relevant in the context of information gain versus disturbance, describes a bound on the resolution of an apparatus measuring simultaneously both the conjugate variables. For a detailed discussion, see K. Wódkiewicz, Phys. Lett. A 124, 207 (1987); S. Stenholm, Ann. Phys. (N.Y.) 218, 233 (1992) and references therein.
4. C. H. Bennett and G. Brassard, in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, India (IEEE, New York, 1984), pp. 175-179.
5. A. K. Ekert, B. Huttner, G. M. Palma, and A. Peres, Phys. Rev. A 50, 1047 (1994); C. A. Fuchs and A. Peres, ibid. 53, 2038 (1996); E. Biham and T. Mor, Phys. Rev. Lett. 78, 2256 (1997); N. Lütkenhaus, Phys. Rev. A 59, 3301 (1999); H. Bechmann-Pasquinucci and N. Gisin, ibid. 59, 4238 (1999).
6. A. K. Ekert, B. Huttner, G. M. Palma, and A. Peres, Phys. Rev. A 50, 1047 (1994); C. A. Fuchs and A. Peres, ibid. 53, 2038 (1996); E. Biham and T. Mor, Phys. Rev. Lett. 78, 2256 (1997); N. Lütkenhaus, Phys. Rev. A 59, 3301 (1999); H. Bechmann-Pasquinucci and N. Gisin, ibid. 59, 4238 (1999).
7. A. K. Ekert, B. Huttner, G. M. Palma, and A. Peres, Phys. Rev. A 50, 1047 (1994); C. A. Fuchs and A. Peres, ibid. 53, 2038 (1996); E. Biham and T. Mor, Phys. Rev. Lett. 78, 2256 (1997); N. Lütkenhaus, Phys. Rev. A 59, 3301 (1999); H. Bechmann-Pasquinucci and N. Gisin, ibid. 59, 4238 (1999).
8. A. K. Ekert, B. Huttner, G. M. Palma, and A. Peres, Phys. Rev. A 50, 1047 (1994); C. A. Fuchs and A. Peres, ibid. 53, 2038 (1996); E. Biham and T. Mor, Phys. Rev. Lett. 78, 2256 (1997); N. Lütkenhaus, Phys. Rev. A 59, 3301 (1999); H. Bechmann-Pasquinucci and N. Gisin, ibid. 59, 4238 (1999).
9. A. K. Ekert, B. Huttner, G. M. Palma, and A. Peres, Phys. Rev. A 50, 1047 (1994); C. A. Fuchs and A. Peres, ibid. 53, 2038 (1996); E. Biham and T. Mor, Phys. Rev. Lett. 78, 2256 (1997); N. Lütkenhaus, Phys. Rev. A 59, 3301 (1999); H. Bechmann-Pasquinucci and N. Gisin, ibid. 59, 4238 (1999).
10. S. Massar and S. Popescu, Phys. Rev. Lett. 74, 1259 (1995); R. Derka, V. Bužek, and A. K. Ekert, ibid. 80, 1571 (1998); G. Vidal, J. I. Latorre, P. Pascual, and R. Tarrach, Phys. Rev. A 60, 126 (1999).
11. S. Massar and S. Popescu, Phys. Rev. Lett. 74, 1259 (1995); R. Derka, V. Bužek, and A. K. Ekert, ibid. 80, 1571 (1998); G. Vidal, J. I. Latorre, P. Pascual, and R. Tarrach, Phys. Rev. A 60, 126 (1999).
12. S. Massar and S. Popescu, Phys. Rev. Lett. 74, 1259 (1995); R. Derka, V. Bužek, and A. K. Ekert, ibid. 80, 1571 (1998); G. Vidal, J. I. Latorre, P. Pascual, and R. Tarrach, Phys. Rev. A 60, 126 (1999).
13. D. Bruss and C. Macchiavello, Phys. Lett. A 253, 149 (1999); A. Acín, J. I. Latorre, and P. Pascual, Phys. Rev. A 61, 022113 (2000).
14. D. Bruss and C. Macchiavello, Phys. Lett. A 253, 149 (1999); A. Acín, J. I. Latorre, and P. Pascual, Phys. Rev. A 61, 022113 (2000).
15. We restrict our attention to the class of ideal operations, which preserve the purity of the state for each conditional transformation. This introduces no loss of generality, as for the purpose of further considerations all nonideal operations can be represented as ideal ones with an additional constraint on the assignment of the guesses to the classical outcomes.
16. K. Banaszek, Phys. Rev. A 62, 024301 (2000).
17. K. E. Atkinson, An Introduction to Numerical Analysis (Wiley, New York, 1978), Sec. 7.2.
18. G. Vidal, D. Jonathan, and M. A. Nielsen, Phys. Rev. A 62, 012304 (2000).
19. M. A Nielsen and C. M. Caves, Phys. Rev. A 55, 2547 (1997).