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

Autor:	Weis, Stephan, Shirokov, Maksim
Rok vydání:	2020
Předmět:	Mathematics - Functional Analysis Mathematical Physics Mathematics - Metric Geometry Quantum Physics 52Axx 47Axx 81Qxx
Zdroj:	Journal of Convex Analysis, 28:3 (2021), 847-870
Druh dokumentu:	Working Paper
Popis:	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. Comment: Any comments are welcome, v2: labels have changed
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2003.14302 Zobrazit plný text záznamu View this record from Arxiv