Distinguishing quantum operations having few kraus operators

Quantum Information and Computation

Volumn 8, Issue 8-9, 2008, Pages 0819-0833

  Watrous, John ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Completely bounded norm; Diamond norm; Quantum channels; Quantum information; Quantum operations

Indexed keywords

AUXILIARY EQUIPMENT; INFORMATION THEORY; QUANTUM CHANNEL; QUANTUM OPTICS;

AUXILIARY SPACE; AUXILIARY SYSTEMS; COMPLETELY BOUNDED; DISTINGUISHABILITY; KRAUS OPERATORS; QUANTUM INFORMATION; QUANTUM OPERATIONS; UNITARY OPERATION;

QUANTUM ENTANGLEMENT;

EID: 65649083671     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. A. Acin. Statistical distinguishability between unitary operations. Physical Review Letters, 87(17):177901, 2001.
2. Aharonov, A. Kitaev, and N. Nisan. Quantum circuits with mixed states. In Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing, pages 20-30, 1998.
3. Barvinok. A Course in Convexity,vo\ume 54 of Graduate Studies in Mathematics.American Mathematical Society, 2002.
4. Ben-Aroya, O. Schwartz, and A. Ta-Shma. An explicit construction of quantum expanders. Available as arXiv.org e-print 0709.0911, 2007.
5. Ben-Aroya and A. Ta-Shma. Quantum expanders and the quantum entropy difference problem. Available as arXiv.org e-print quant-ph/0702129, 2007.
6. Childs, J. Preskill, and J. Renes. Quantum information and precision measurement. Journal of Modern Optics, 47(2-3):155-176, 2000. (Pubitemid 35392904)
7. D'Ariano, P. Presti, and M. Paris. Using entanglement improves the precision of quantum measurements. Physical Review Letters, 87(27):270404, 2001. (Pubitemid 34047375)
8. Gilchrist, N. Langford, and M. Nielsen. Distance measures to compare real and ideal quantum processes. Physical Review A, 71:062310, 2005.
9. Gross and J. Eisert. Quantum Margulis expanders. Available as arXiv.org e-print 0710.0651, 2007.
10. A. Harrow. Quantum expanders from any classical Cayley graph expander. Available as arXiv.org e-pr0int 0709.1142, 2007.
11. M. Hastings. Entropy and entanglement in quantum ground states. Physical Review B, 76:035114, 2007.
12. M. Hastings. Random unitaries give quantum expenders. Physical Review A, 76:032315, 2007. (Pubitemid 47429353)
13. P. Hayden, D. Leung, P. Shor, and A. Winter. Randomizing quantum states: Constructions and applications. Communications in Mathematical Physics, 250(2):371-391, 2004. (Pubitemid 39374478)
14. A. Kitaev. Quantum computations: algorithms and error correction. Russian Mathematical Surveys, 52(6):1191-1249, 1997. (Pubitemid 127374800)
15. A. Kitaev, A. Shen, and M. Vyalyi. Classical and Quantum Computation,vo\ume 47 of Graduate Studies in Mathematics. American Mathematical Society, 2002.
16. A. Kitaev and J. Watrous. Parallelization, amplification, and exponential time simulation of quantum interactive proof system. In Proceedings of the 32nd ACM Symposium on Theory of Computing, pages 608-617, 2000.
17. D. Kretschmann, D. Schlingemann, and R. Werner. The information- disturbance tradeoff and the continuity of Stinespring's representation. Available as arXiv.org e-print quant-ph/0605009, 2006.
18. M. Nielsen and I. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2000.
19. V. Paulsen. Completely Bounded Maps and Operator Algebras. Cambridge Studies in Advanced Mathematics. Cambridge University Press, 2002.
20. B. Rosgen and J. Watrous. On the hardness of distinguishing mixed-state quantum computations. In Proceedings of the 20th Annual Conference on Computational Complexity, pages 344-354, 2005.
21. M. Sacchi. Entanglement can enhance the distinguishability of entanglement-breaking channels. Physical Review A, 72:014305, 2005. (Pubitemid 43272599)
22. M. Sacchi. Optimal discrimination of quantum operations. Physical Review A, 71:062340, 2005.
23. R. Smith. Completely bounded maps between C-algebras. Journal of the London Mathematical Society, 2(1):157-166, 1983.
24. R. Timoney. Computing the norms of elementary operators. Illinois Journal of Mathematics, 47(4):1207-1226, 2003. (Pubitemid 38390216)
25. R. Timoney. Some formulae for norms of elementary operators. Journal of Operator Theory, 57(1):121-145, 2007.
26. J. Watrous. Notes on super-operator norms induced by Schatten norms. Quantum Information and Computation, 5(1):58-68, 2005. (Pubitemid 40344869)