Positive maps, positive polynomials and entanglement witnesses
Łukasz Skowronek, Karol Życzkowski · Journal of Physics A Mathematical and Theoretical · 2009
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.