Classical deterministic complexity of Edmonds' Problem and quantum entanglement

  title={Classical deterministic complexity of Edmonds' Problem and quantum entanglement},
  author={Leonid I. Gurvits},
  booktitle={STOC '03},
  • L. Gurvits
  • Published in STOC '03 11 March 2003
  • Mathematics
Generalizing a decision problem for bipartite perfect matching, J. Edmonds introduced in [14] the problem (now known as the Edmonds Problem) of deciding if a given linear subspace of M(N) contains a nonsingular matrix, where M(N) stands for the linear space of complex NxN matrices. This problem led to many fundamental developments in matroid theory etc.Classical matching theory can be defined in terms of matrices with nonnegative entries. The notion of Positive operator, central in Quantum… 
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  • L. Ioannou
  • Computer Science
    Quantum Inf. Comput.
  • 2007
This paper gives the first systematic and comprehensive treatment of this (bipartite) quantum separability problem, focusing on its deterministic computational complexity.