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States and Positive Maps

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Positive Linear Maps of Operator Algebras

Part of the book series: Springer Monographs in Mathematics ((SMM))

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Abstract

In this chapter we apply the results on dual functionals of positive maps to study states on tensor products of full matrix algebras. In particular we obtain characterizations of separable and PPT-states, and we also see how entanglement is related to the negative part of the Choi matrix of a positive map. Some of these ideas will be used to study the celebrated Choi map of the 3×3 matrices into themselves. Finally it is shown that the dual functional of the sum of the trace and a positive map of norm 1 is separable.

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Authors and Affiliations

  1. Department of Mathematics, University of Oslo, Oslo, Norway

    Erling Størmer

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  1. Erling Størmer
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Størmer, E. (2013). States and Positive Maps. In: Positive Linear Maps of Operator Algebras. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34369-8_7

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