Schmidt states and positivity of linear maps

Aik-meng Kuah; E. C. G. Sudarshan

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Schmidt states and positivity of linear maps

Aik-meng Kuah·E. C. G. Sudarshan

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Abstract

Using pure entangled Schmidt states, we show that m-positivity of a map is bounded by the ranks of its negative Kraus matrices. We also give an algebraic condition for a map to be m-positive. We interpret these results in the context of positive maps as entanglement witnesses, and find that only 1-positive maps are needed for testing entanglement.

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Aik-meng Kuah, E. C. G. Sudarshan. 2005-06-13. Schmidt states and positivity of linear maps. https://arxiv.org/abs/quant-ph/0506095

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