Related papers: The face generated by a point, generalized affine constraints, and quantum theory

The face generated by a point, generalized affine constraints, and quantum theory

URL: http://arxiv.org/abs/2003.14302v2
Date: Thu, 4 Jun 2020 21:56:15 GMT
Title: The face generated by a point, generalized affine constraints, and quantum theory
Authors: Stephan Weis and Maksim Shirokov
Abstract summary: We show that by intersecting a convex set with a sublevel or level set of a generalized affine functional, the dimension of the face generated by a point may decrease by at most one. We apply the results to the set of quantum states on a separable Hilbert space.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We analyze faces generated by points in an arbitrary convex set and their relative algebraic interiors, which are nonempty as we shall prove. We show that by intersecting a convex set with a sublevel or level set of a generalized affine functional, the dimension of the face generated by a point may decrease by at most one. We apply the results to the set of quantum states on a separable Hilbert space. Among others, we show that every state having finite expected values of any two (not necessarily bounded) positive operators admits a decomposition into pure states with the same expected values. We discuss applications in quantum information theory.

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