Entropy 2010, 12(6), 1612-1631; doi:10.3390/e12061612
Article

Eigenvalue and Entropy Statistics for Products of Conjugate Random Quantum Channels

1 Department of Mathematics and Statistics, University of Ottawa, ON, Canada 2 CNRS, Institut Camille Jordan, Université Lyon 1, France
* Author to whom correspondence should be addressed.
Received: 4 May 2010; in revised form: 17 June 2010 / Accepted: 18 June 2010 / Published: 23 June 2010
(This article belongs to the Special Issue Quantum Information)
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Abstract: 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.
Keywords: random quantum channels; weingarten calculus; minimum output entropy; von neumann entropy; additivity problem

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MDPI and ACS Style

Collins, B.; Nechita, I. Eigenvalue and Entropy Statistics for Products of Conjugate Random Quantum Channels. Entropy 2010, 12, 1612-1631.

AMA Style

Collins B, Nechita I. Eigenvalue and Entropy Statistics for Products of Conjugate Random Quantum Channels. Entropy. 2010; 12(6):1612-1631.

Chicago/Turabian Style

Collins, Benoît; Nechita, Ion. 2010. "Eigenvalue and Entropy Statistics for Products of Conjugate Random Quantum Channels." Entropy 12, no. 6: 1612-1631.

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