Positive maps, positive polynomials and entanglement witnesses

Details Positive maps, positive polynomials and entanglement witnesses Positive maps, positive polynomials and entanglement witnesses

2009-03-17

arxiv.org/abs/0903.3042v1

J. Phys. A: Math. Theor. 42 (2009) 325302

Physics

Mathematical Physics

17 pages, 1 figure

Scientific paper

10.1088/1751-8113/42/32/325302

We link the study of positive quantum maps, block positive operators, and entanglement witnesses with problems related to multivariate polynomials. For instance, we show how indecomposable block positive operators relate to biquadratic forms that are not sums of squares. Although the general problem of describing the set of positive maps remains open, in some particular cases we solve the corresponding polynomial inequalities and obtain explicit conditions for positivity.

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