An efficient test for product states, with applications to quantum Merlin-Arthur games

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

Volumn , Issue , 2010, Pages 633-642

  Harrow, Aram W ^a,b   Montanaro, Ashley ^a,c  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b UNIVERSITY OF WASHINGTON   (United States)

^c UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COMMUNICATION CHANNELS (INFORMATION THEORY); POLYNOMIAL APPROXIMATION; QUANTUM OPTICS; TESTING;

INDIVIDUAL SYSTEMS; LINEARITY TESTING; MAXIMUM OUTPUT; POLYNOMIAL-TIME ALGORITHMS; QUANTUM ALGORITHMS; QUANTUM SYSTEM; TENSOR PRODUCTS; UNITARY OPERATORS;

QUANTUM EFFICIENCY;

EID: 78751532788     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FOCS.2010.66     Document Type: Conference Paper

References (43)

1. D. P. DiVincenzo, P. W. Shor, and J. A. Smolin, "Quantum channel capacity of very noisy channels," Phys. Rev. A., vol. 57, p. 830, 1998, quant-ph/9706061.
2. M. B. Hastings, "A counterexample to additivity of minimum output entropy," Nature Physics, vol. 5, 2009, arXiv:0809. 3972.
3. T. Ito, H. Kobayashi, and K. Matsumoto, "Oracularization and two-prover one-round interactive proofs against nonlocal strategies," 2008, arXiv:0810.0693.
4. H. Kobayashi, K. Matsumoto, and T. Yamakami, "Quantum Merlin-Arthur proof systems: are multiple Merlins more helpful to Arthur?" in Proc. ISAAC '03, 2003, pp. 189-198, quant-ph/0306051.
5. S. Aaronson, S. Beigi, A. Drucker, B. Fefferman, and P. Shor, "The power of unentanglement," Theory of Computing, vol. 5, no. 1, pp. 1-42, 2009, arXiv:0804.0802.
6. J. Kempe and O. Regev, "No strong parallel repetition with entangled and non-signaling provers," 2009, arXiv:0911.0201.
7. T. Ogawa and H. Nagaoka, "Strong converse to the quantum channel coding theorem," IEEE Trans. Inform. Theory, vol. 45, no. 7, pp. 2486-2489, 1999, quant-ph/9808063.
8. A. Winter, "Coding theorem and strong converse for quantum channels," IEEE Trans. Inform. Theory, vol. 45, no. 7, pp. 2481-2485, 1999.
9. E. Fischer, "The art of uninformed decisions: A primer to property testing," Bulletin of the European Association for Theoretical Computer Science, vol. 75, pp. 97-126, 2001.
10. H. Buhrman, L. Fortnow, I. Newman, and H. Röhrig, "Quantum property testing," SIAM J. Comput., vol. 37, no. 5, pp. 1387-1400, 2008, quant-ph/0201117.
11. A. Atici and R. A. Servedio, "Quantum algorithms for learning and testing juntas," Quantum Information Processing, vol. 6, pp. 323-348, 2007, arXiv:0707.3479.
12. A. Montanaro and T. Osborne, "Quantum boolean functions," Chicago Journal of Theoretical Computer Science, vol. to appear, 2010, arXiv:0810.2435.
13. S. Aaronson, "The learnability of quantum states," Proceedings of the Royal Society A, vol. 463, p. 2088, 2007, quant-ph/0608142.
14. O. Gühne and G. Toth, "Entanglement detection," Physics Reports, vol. 471, no. 1, 2009, arXiv:0811.2803.
15. H. Buhrman, R. Cleve, J. Watrous, and R. de Wolf, "Quantum fingerprinting," Phys. Rev. Lett., vol. 87, no. 16, p. 167902, 2001, quant-ph/0102001.
16. F. Mintert, M. Kuś, and A. Buchleitner, "Concurrence of mixed multipartite quantum states," Phys. Rev. Lett., vol. 95, no. 26, p. 260502, 2005, quant-ph/0411127.
17. S. Walborn, P. Ribeiro, L. Davidovich, F. Mintert, and A. Buchleitner, "Experimental determination of entanglement with a single measurement," Nature, vol. 440, no. 7087, pp. 1022-1024, 2006.
18. th Annual ACM Symp. Theory of Computing, 2003, pp. 10-19, quant-ph/ 0303055.
19. S. Gharibian, "Strong NP-hardness of the quantum separability problem," Quantum Inf. Comput., vol. 10, no. 3&4, pp. 343-360, 2010, arXiv:0810.4507.
20. G. G. Amosov, A. S. Holevo, and R. F. Werner, "On some additivity problems in quantum information theory," Problems Inform. Transmission, vol. 36, no. 4, pp. 305-313, 2000, arXiv:math-ph/0003002.
21. H. Blier and A. Tapp, "All languages in NP have very short quantum proofs," in First International Conference on Quantum, Nano, and Micro Technologies. Los Alamitos, CA, USA: IEEE Computer Society, 2009, pp. 34-37.
22. Y.-K. Liu, "The complexity of the consistency and N-representability problems for quantum states," Ph.D. dissertation, Univ. of California, San Diego, 2007.
23. M. Blum, M. Luby, and R. Rubinfeld, "Self-testing/correcting with applications to numerical problems," J. Comput. Syst. Sci., vol. 47, no. 3, pp. 549-595, 1993.
24. T. Wei and P. Goldbart, "Geometric measure of entanglement and applications to bipartite and multipartite quantum states," Phys. Rev. A., vol. 68, no. 4, p. 42307, 2003, quant-ph/ 0307219.
25. A. W. Harrow and A. Montanaro, "An efficient test for product states, with applications to quantum Merlin-Arthur games," 2010, arXiv:1001.0017.
26. A. Barenco, A. Berthiaume, D. Deutsch, A. Ekert, R. Jozsa, and C. Macchiavello, "Stabilisation of quantum computations by symmetrisation," SIAM J. Comput., vol. 26, no. 5, pp. 1541-1557, 1997, quant-ph/9604028.
27. F. Brandão, "Entanglement theory and the quantum simulation of many-body physics," Ph.D. dissertation, Imperial College, London, 2008, arXiv:0810.0026.
28. R. Impagliazzo and R. Paturi, "On the complexity of k-SAT," J. Comput. Syst. Sci., vol. 62, no. 2, pp. 367-375, 2001.
29. M. Grötschel, L. Lovász, and A. Schrijver, Geometric algorithms and combinatorial optimization. Springer-Verlag, 1993.
30. S. Beigi, "NP vs QMA log(2)," Quantum Inf. Comput., vol. 10, no. 1&2, 2010, arXiv:0810.5109.
31. P. W. Shor, "Equivalence of additivity questions in quantum information theory," Comm. Math. Phys., vol. 246, no. 3, pp. 453-472, 2004, quant-ph/0305035.
32. S. Beigi and P. Shor, "On the complexity of computing zero-error and Holevo capacity of quantum channels," 2007, arXiv: 0709.2090.
33. K. Matsumoto, "Some new results and applications of additivity problem of quantum channel," Poster at QIP'05 conference, 2005.
34. R. König and S. Wehner, "A strong converse for classical channel coding using entangled inputs," Phys. Rev. Lett., vol. 103, p. 070504, 2009, arXiv:0903.2838.
35. R. König, S. Wehner, and J. Wullschleger, "Unconditional security from noisy quantum storage," 2009, arXiv:0906.1030.
36. P. Hayden and A. Winter, "Counterexamples to the maximal p-norm multiplicativity conjecture for all p > 1," Comm. Math. Phys., vol. 284, no. 1, pp. 263-280, 2008.
37. T. Cubitt, A. W. Harrow, D. Leung, A. Montanaro, and A. Winter, "Counterexamples to additivity of minimum output p-Renyi entropy for p close to 0," Comm. Math. Phys., vol. 284, pp. 281-290, 2008, arXiv:0712.3628.
38. G. Vidal and J. I. Cirac, "Irreversibility in asymptotic manipulations of entanglement," Phys. Rev. Lett., vol. 86, p. 022308, 2001, quant-ph/0102036.
39. D. Yang, M. Horodecki, R. Horodecki, and B. Synak-Radtke, "Irreversibility for all bound entangled states," Phys. Rev. Lett., vol. 95, p. 190501, 2005, quant-ph/0506138.
40. I. Devetak, M. Junge, C. King, and M. B. Ruskai, "Multiplicativity of completely bounded p-norms implies a new additivity result," Comm. Math. Phys., vol. 266, pp. 37-63, 2006, quant-ph/0506196.
41. D. Yang, M. Horodecki, and Z. D. Wang, "An additive and operational entanglement measure: conditional entanglement of mutual information," Phys. Rev. Lett., vol. 101, p. 140501, 2008, arXiv:0804.3683.
42. M. Fannes and C. Vandenplas, "Finite size mean-field models," J. Phys. A: Math. Gen., vol. 39, no. 45, p. 13843, 2006, quant-ph/0605216.
43. st Annual ACM Symp. Theory of Computing. New York, NY, USA: ACM, 2009, pp. 417-426, arXiv:0811.3412.