Random matrix techniques in quantum information theory

Journal Article · Fri Jan 15 00:00:00 EST 2016 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4936880· OSTI ID:22479619

Collins, Benoît ^[1]; CNRS, Lyon ^[2]; Nechita, Ion ^[3]

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1. Department of Mathematics, Kyoto University, Kyoto 606-8502 (Japan)
2. France
3. Zentrum Mathematik, M5, Technische Universität München, Boltzmannstrasse 3, 85748 Garching (Germany)

The purpose of this review is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review and of more detailed examples—coming mainly from research projects in which the authors were involved. We focus on two main topics, random quantum states and random quantum channels. We present results related to entropic quantities, entanglement of typical states, entanglement thresholds, the output set of quantum channels, and violations of the minimum output entropy of random channels.

• OSTI ID: 22479619
• Journal Information: Journal of Mathematical Physics, Vol. 57, Issue 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ENTROPY
MATRICES
QUANTUM ENTANGLEMENT
QUANTUM INFORMATION
QUANTUM STATES
RANDOMNESS