A problem of existence of bound entangled states with non-positive partial transpose and the Hilbert's 17th problem
Quantum Physics
2010-07-13 v1
Abstract
It is found that the problem of existence of bound entangled states with non-positive partial transpose (NPPT) has the intriguing relation to the Hilbert's 17th problem. More precisely, we compute the expectation value of the partially transposed Werner states by Schmidt rank-2 vectors for NPPT and 1-copy undistillable region. It is the positive polynomial but shown not to be expressed as the sum of squares of polynomials. A remedy for such pathological behavior as well as a similar but different approach to the problem is also mentioned.
Keywords
Cite
@article{arxiv.1007.1830,
title = {A problem of existence of bound entangled states with non-positive partial transpose and the Hilbert's 17th problem},
author = {Tohya Hiroshima},
journal= {arXiv preprint arXiv:1007.1830},
year = {2010}
}
Comments
9 pages, no figures