Facial structures for various notions of positivity and applications to the theory of entanglement
classification
🪐 quant-ph
keywords
positivelinearmapsentanglementfacialnotionsstructuresalgebras
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In this expository note, we explain facial structures for the convex cones consisting of positive linear maps, completely positive linear maps, decomposable positive linear maps between matrix algebras, respectively. These will be applied to study the notions of entangled edge states with positive partial transposes and optimality of entanglement witnesses.
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