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

Article

Eigenvalue and Entropy Statistics for Products of Conjugate Random Quantum Channels

Benoît Collins ^1,2  and Ion Nechita ^1,*

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)

Download PDF Full-Text [676 KB, uploaded 23 June 2010 10:40 CEST]

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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