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Eigenvalue and entropy statistics for products of conjugate random quantum channels. (English) Zbl 1229.81044

Summary: Using the graphical calculus and integration techniques introduced by the authors, we study the statistical properties of outputs of products of random quantum channels for entangled inputs. In particular, we revisit and generalize models of relevance for the recent counterexamples to the minimum output entropy additivity problems. Our main result is a classification of regimes for which the von Neumann entropy is lower on average than the elementary bounds that can be obtained with linear algebra techniques.

MSC:

81P45 Quantum information, communication, networks (quantum-theoretic aspects)
94A40 Channel models (including quantum) in information and communication theory
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