Implements PnCP maps from non-SOS polynomials, proves they are indecomposable and boundary-localized, shows inequivalence to most known maps, and demonstrates detection of PPT entangled states missed by other criteria.
Positive maps, positive polynomials and entanglement witnesses
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abstract
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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quant-ph 1years
2026 1verdicts
CONDITIONAL 1representative citing papers
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Detecting bipartite entanglement with PnCP maps and non-negative polynomials
Implements PnCP maps from non-SOS polynomials, proves they are indecomposable and boundary-localized, shows inequivalence to most known maps, and demonstrates detection of PPT entangled states missed by other criteria.