Criterion of weak compactness for families of generalized ensembles and its corollaries. (English. Russian original) Zbl 1339.81014

Theory Probab. Appl. 60, No. 2, 320-325 (2016); translation from Teor. Veroyatn. Primen. 60, No. 2, 402-408 (2015).
Summary: One of the central results of the theory of probability measures on metric spaces is Prokhorov’s theorem on weak compactness of a subset of probability measures. In the present paper this theorem is used to obtain a criterion of weak compactness for families of generalized quantum ensembles, i.e., Borel probability measures on the set of quantum states, and its applications in quantum information theory are considered.


81P16 Quantum state spaces, operational and probabilistic concepts
81P45 Quantum information, communication, networks (quantum-theoretic aspects)
94A40 Channel models (including quantum) in information and communication theory
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