On the hardness of distinguishing mixed-state quantum computations

Proceedings of the Annual IEEE Conference on Computational Complexity

Volumn , Issue , 2005, Pages 344-354

  Rosgen, Bill ^a   Watrous, John ^b  

^a UNIVERSITY OF ALBERTA   (Canada)

^b UNIVERSITY OF CALGARY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

DISCRETE QUANTUM MECHANICAL PROCESS; QUANTUM COMPUTATIONS; QUANTUM INTERACTIVE PROOF SYSTEMS; UNITARY QUANTUM CIRCUITS;

NETWORKS (CIRCUITS); PROBLEM SOLVING;

QUANTUM THEORY;

EID: 27644510466     PISSN: 10930159     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CCC.2005.21     Document Type: Conference Paper

References (15)

1. D. Aharonov, A. Kitaev, and N. Nisan. Quantum circuits with mixed states. In Proceedings of the 30th Annual ACM Symposium on Theory of Computing, pages 20-30, 1998.
2. A. Ambainis, L. Schulman, and U. Vazirani. Computing with highly mixed states. In Proceedings of the 32nd Annual ACM Symposium on the Theory of Computing, 2000.
3. M.-D. Choi. Completely positive linear maps on complex matrices. Linear Algebra and its Applications, 10(3):285-290, 1975.
4. D. Janzing, P. Wocjan, and T. Beth. "Identity check" is QMA-complete. arXiv.org e-Print quant-ph/0305050, 2003.
5. A. Kitaev. Quantum computations: algorithms and error correction. Russian Mathematical Surveys, 52(6): 1191-1249, 1997.
6. A. Kitaev, A. Shen, and M. Vyalyi. Classical and Quantum Computation, volume 47 of Graduate Studies in Mathematics. American Mathematical Society, 2002.
7. A. Kitaev and J. Watrous. Parallelization, amplification, and exponential time simulation of quantum interactive proof system. In Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, pages 608-617, 2000.
8. E. Knill and R. Laflamme. On the power of one bit of quantum information. Physical Review Letters, 81:5672-5675, 1998.
9. A. Kondacs and J. Watrous. On the power of quantum finite state automata. In Proceedings of the 38th Annual Symposium on Foundations of Computer Science, pages 66-75, 1997.
10. C. Moore and J. Crutchfield. Quantum automata and quantum grammars. Theoretical Computer Science, 237:275-306, 2000.
11. M. A. Nielsen and I. L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2000.
12. A. Sahai and S. Vadhan. A complete promise problem for statistical zero-knowledge. Journal of the ACM, 50(2):196-249, 2003.
13. I. Watrous. Limits on the power of quantum statistical zero-knowledge. In Proceedings of the 43rd Annual Symposium on Foundations of Computer Science, pages 459-468, 2002.
14. J. Watrous. PSPACE has constant-round quantum interactive proof systems. Theoretical Computer Science, 292(3):575-588, 2003.
15. J. Watrous. Notes on super-operator norms induced by Schatten norms. Quantum Information and Computation, 5(1):58-68, 2005.