| Classical deterministic complexity of Edmonds' problem and Quantum Entanglement (2003) | |||||||||
Abstract | |||||||||
| This paper continues research initiated in quant-ph/0201022 . The main subject here is the so-called Edmonds' problem of deciding if a given linear subspace of square matrices contains a nonsingular matrix . We present a deterministic polynomial time algorithm to solve this problem for linear subspaces satisfying a special matroids motivated property, called in the paper the Edmonds-Rado property . This property is shown to be very closely related to the separability of bipartite mixed states . One of the main tools used in the paper is the Quantum Permanent introduced in quant-ph/0201022 .. Comment: 31 pages, long version of STOC-2003 paper | |||||||||
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