Classical deterministic complexity of Edmonds' problem and quantum entanglement

Conference Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2003, Pages 10-19

  Gurvits, Leonid ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

Algorithms; Theory

Indexed keywords

ALGORITHMS; COMPUTATIONAL GEOMETRY; MATRIX ALGEBRA; PROBLEM SOLVING;

DECISION PROBLEM;

QUANTUM THEORY;

EID: 0041345998     PISSN: 07349025     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/780542.780545     Document Type: Conference Paper

References (28)

1. D. Zeilberger, CHu's 1303 identity implies Bombieri's 1990 norm-inequality [Via an identity of Beauzamy and Degot], Amer. Math. Monthly, 1994.
2. B. Beauzamy, E. Bombieri, P. Enflo, H.L. Montgomery, Products of polynomials in many variables, Journal of Number Theory 36, 219-245, 1990.
3. B. Reznick, An inequality for products of polynomials, Proc. of AMS, vol. 117, Is. 4, 1063-1073, 1993.
4. B. Beauzamy, Products of polynomials and a priori estimates for coefficients in polynomial decompositions: A sharp result, J. Symbolic Computation 13 (1992), 463-472.
5. A.Nemirovski, Personal Communication, 2001.
6. V.Kabanets and R.Impagliazzo, Derandomizing polynomial identity tests means proving circuit lower bounds, Electronic Colloq. on Comp. Complex, No. 55, 2002.,
7. L.Gurvits, Quantum Matching Theory (with new complexity-theoretic, combinatorial and topological insights on the nature of the Quantum Entanglement), arXiv.org preprint quant-ph/02010222, 2002.
8. L.Gurvits, Classical deterministic complexity of Edmonds' problem and Quantum Entanglement, arXiv.org preprint quant-ph/0303055, 2003.
9. L.Gurvits, Unbiased nonnegative valued random estimator for permanents of complex positive semidefinite matrices, LANL unclassified report LAUR 02-5166, 2002.
10. H.Minc, Permanents, Addison - Wesley, Reading, MA, 1978.
11. R. B. Bapat, Mixed discriminants of positive semidefinite matrices, Linear Algebra and its Applications 126, 107-124, 1989.
12. A. Ben-Tal and A.Nemirovski, Robust convex optimization, Mathematics of Operational Research, Vol. 23, 4 (1998), 769-805.
13. D.B.Yudin and A.S. Nemirovskii, Informational complexity and efficient methods for the solution of convex extremal problems (in Russian), Ekonomica i Matematicheskie Metody 12 (1976), 357-369.
14. J. Edmonds, System of distinct representatives and linear algebra, Journal of Research of the National Bureau of Standards 718, 4(1967), 242-245.
15. A. Chistov, G. Ivanyos, M. Karpinski, Polynomial time algorithms for modules over finite dimensional algebras, Proc. of ISSAC'97, pp. 68-74, Maui, Hawaii, USA, 1997.
16. A. I. Barvinok, Computing Mixed Discriminants, Mixed Volumes, and Permanents, Discrete & Computational Geometry, 18 (1997), 205-237.
17. A. I. Barvinok, Polynomial time algorithms to approximate permanents and mixed discriminants within a simply exponential factor, Random Structures & Algorithms, 14 (1999), 29-61.
18. G.P. Egorychev, The solution of van der Waerden's problem for permanents, Advances in Math., 42, 299-305, 1981.
19. D. I. Falikman, Proof of the van der Waerden's conjecture on the permanent of a doubly stochastic matrix, Mat. Zametki 29, 6: 931-938, 957, 1981, (in Russian).
20. M. Grötschel, L. Lovasz and A. Schrijver, Geometric Algorithms and Combinatorial Optimization, Springer-Verlag, Berlin, 1988.
21. L. Gurvits, Van der Waerden Conjecture for Mixed Discriminants, submitted, 2000; accepted for publication in Advances in Mathematics, 2001.
22. A.Zvonkin, Matrix integral and map enumeration: an accessible introduction, Mathl. Comput. Modelling, Vol. 26, No. 8-10, pp. 281-304, 1997.
23. N. Linial, A. Samorodnitsky and A. Wigderson, A deterministic strongly polynomial algorithm for matrix scaling and approximate permanents, Proc. 30 ACM Symp. on Theory of Computing, ACM, New York, 1998.
24. L.Gurvits and A. Samorodnitsky, A deterministic polynomial-time algorithm for approximating mised discriminant and mixed volume, Proc. 32 ACM Symp. on Theory of Computing, ACM, New York, 2000.
25. L.Gurvits and A. Samorodnitsky, A deterministic algorithm approximating the mixed discriminant and mixed volume, and a combinatorial corollary, Discrete Comput. Geom. 27: 531 -550, 2002 /
26. L.Gurvits and P.Yianilos, The deflation-inflation method for certain semidefinite programming and maximum determinant completion problems, NECI technical report, 1998.
27. J. Forster, A Linear Lower Bound on the Unbounded Error Probabilistic Communication Complexity, Sixteenth Annual IEEE Conference on Computational Complexity, 2001.
28. L.Gurvits and H.Barnum, Largest separable balls around the maximally mixed bipartite quantum state," Phys. Rev. A 66 062311 (2002).