Some properties of partial fidelities

Quantum Information and Computation

Volumn 9, Issue 11-12, 2009, Pages 1069-1080

  Rastegin, Alexey E ^a  

^a IRKUTSK STATE UNIVERSITY   (Russian Federation)

Author keywords

Ky fan's maximum principle; Quantum fidelity; Quantum measurement; Quantum operation; Submultiplicativity

Indexed keywords

DISTINGUISHABILITY; KY FAN MAXIMUM PRINCIPLE; PROPERTY; QUANTUM FIDELITY; QUANTUM MEASUREMENT; QUANTUM OPERATIONS; STATISTICAL INTERPRETATION; SUBMULTIPLICATIVITY; TRACE DISTANCES;

EID: 71549124973     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: 10.26421/qic9.11-12-9     Document Type: Article

References (29)

1. A.Uhlmann (1976), The transition probability in the state space of a *-algebra, Rep. Math. Phys. 9, pp. 273-279.
2. P. M. Alberti and A. Uhlmann (1983), Stochastic linear maps and transition probability, Lett. Math. Phys. 7, pp. 107-112.
3. R. Jozsa (1994), Fidelity for mixed quantum states, J. Mod. Opt. 41, pp. 2315-2323.
4. M. A. Nielsen and I. L. Chuang (2000), Quantum computation and quantum information, Cambridge University Press (Cambridge).
5. A. Gilchrist, N. K. Langford and M. A. Nielsen (2005), Distance measures to compare real and ideal quantum processes, Phys. Rev. A 71, 062310.
6. S. L. Braunstein and C. M. Caves (1995), Geometry of quantum states, Proceedings of the Conference on Quantum Communication and Measurement, edited by R. Hudson, V. P. Belavkin, O. Hirota, New York (Plenum Press), pp. 21-30.
7. I. Bengtsson and K. Zyczkowski (2006), Geometry of quantum states: an introduction to quantum entanglement, Cambridge University Press (Cambridge).
8. V. Giovannetti and A. S. Holevo (2008), Quantum Shared Broadcasting, Quantum Information Processing 7, pp. 55-69.
9. M. R. Dowling and M. A. Nielsen (2008), The geometry of quantum computation, Quantum Information & Computation 8, pp. 861-899.
10. C. A. Fuchs (1996), Distinguishability and accessible information in quantum theory, quantph/9601020.
11. A. Uhlmann (2000), On "partial" fidelities, Rep. Math. Phys. 45, pp. 407-418.
12. P. E. M. F. Mendonça, R. J. Napolitano, M. A. Marchiolli, C. J. Foster and Y.-C. Liang (2008), Alternative fidelity measure between quantum states, Phys. Rev. A 78, 052330.
13. J. A. Miszczak, Z. Puchala, P. Horodecki, A. Uhlmann and K. Zyczkowski (2009), Sub- and super-fidelity as bounds for quantum fidelity, Quantum Information & Computation 9, pp. 0103-0130.
14. A. E. Rastegin (2003), Upper bound on the global fidelity for mixed-state cloning, Phys. Rev. A 68, 012305.
15. K. Zyczkowski and W. Słomczyński (1998), The Monge distance between quantum states, J. Phys. A: Math. Gen. 31, pp. 9095-9104.
16. A. E. Rastegin (2006), Sine distance for quantum states, quant-ph/0602112.
17. J. Watrous (2008), CS 798: Theory of quantum information, University of Waterloo, http://www.cs.uwaterloo.ca/-watrous/quant-info/lecture-notes/all- lectures.pdf.
18. R. Bhatia (1997), Matrix Analysis, Springer (New York).
19. C. A. Fuchs and C. M. Caves (1995), Mathematical techniques for quantum communication theory, Open Systems & Information Dynamics 3, pp. 345-356.
20. A. E. Rastegin (2003), Global-fidelity limits of state-dependent cloning of mixed states, Phys. Rev. A 68, 032303.
21. P. M. Alberti and A. Uhlmann (2000), On Bures distance and *-algebraic transition probability between inner derived positive linear forms over W*-algebras, Acta Applicandae Mathematicae 60, pp. 1-37.
22. A. Peres (1993), Quantum theory: concepts and methods, Kluwer (Dordrecht).
23. K. Fan (1949), On a theorem of Weyl concerning eigenvalues of linear transformations. I, Proc. Nat. Acad. Sci. U.S.A. 35, pp. 652-655.
24. M. A. Nielsen and G. Vidal (2001), Majorization and the interconversion of bipartite states, Quantum Information & Computation 1, pp. 76-93.
25. H. Barnum, C. M. Caves, C. A. Fuchs, R. Jozsa and B. Schumacher (1996), Noncommuting mixed states cannot be broadcast, Phys. Rev. Lett. 76, pp. 2818-2821.
26. Z. Puchala and J. A. Miszczak (2009), Bound on trace distance based on super-fidelity, Phys. Rev. A 76, 024302.
27. A. E. Rastegin (2009), Partitioned trace distances, arXiv:0903.4543 [quant-ph].
28. C. A. Fuchs and J. van de Graaf (1999), Cryptographic distinguishability measures for quantum mechanical states, IEEE Trans. Inf. Theory 45, pp. 1216-1227.
29. A. E. Rastegin (2007), Trace distance from the viewpoint of quantum operation techniques, J. Phys. A: Math. Theor. 40, 9533-9549.