On the Separability of Unitarily Invariant Random Quantum States: The Unbalanced Regime

On the Separability of Unitarily Invariant Random Quantum States: The Unbalanced Regime

We study entanglement-related properties of random quantum states which are unitarily invariant, in the sense that their distribution is left unchanged by conjugation with arbitrary unitary operators. In the large matrix size limit, the distribution of these random quantum states is characterized by...

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Main Author: Ion Nechita
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2018/7105074
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spelling doaj-929e629219b34fbda7d6668a789ee90e2021-07-02T14:12:05ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/71050747105074On the Separability of Unitarily Invariant Random Quantum States: The Unbalanced RegimeIon Nechita0Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, Toulouse, FranceWe study entanglement-related properties of random quantum states which are unitarily invariant, in the sense that their distribution is left unchanged by conjugation with arbitrary unitary operators. In the large matrix size limit, the distribution of these random quantum states is characterized by their limiting spectrum, a compactly supported probability distribution. We prove several results characterizing entanglement and the PPT property of random bipartite unitarily invariant quantum states in terms of the limiting spectral distribution, in the unbalanced asymptotical regime where one of the two subsystems is fixed, while the other one grows in size.http://dx.doi.org/10.1155/2018/7105074
collection DOAJ
language English
format Article
sources DOAJ
author Ion Nechita
spellingShingle Ion Nechita
On the Separability of Unitarily Invariant Random Quantum States: The Unbalanced Regime
Advances in Mathematical Physics
author_facet Ion Nechita
author_sort Ion Nechita
title On the Separability of Unitarily Invariant Random Quantum States: The Unbalanced Regime
title_short On the Separability of Unitarily Invariant Random Quantum States: The Unbalanced Regime
title_full On the Separability of Unitarily Invariant Random Quantum States: The Unbalanced Regime
title_fullStr On the Separability of Unitarily Invariant Random Quantum States: The Unbalanced Regime
title_full_unstemmed On the Separability of Unitarily Invariant Random Quantum States: The Unbalanced Regime
title_sort on the separability of unitarily invariant random quantum states: the unbalanced regime
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2018-01-01
description We study entanglement-related properties of random quantum states which are unitarily invariant, in the sense that their distribution is left unchanged by conjugation with arbitrary unitary operators. In the large matrix size limit, the distribution of these random quantum states is characterized by their limiting spectrum, a compactly supported probability distribution. We prove several results characterizing entanglement and the PPT property of random bipartite unitarily invariant quantum states in terms of the limiting spectral distribution, in the unbalanced asymptotical regime where one of the two subsystems is fixed, while the other one grows in size.
url http://dx.doi.org/10.1155/2018/7105074
work_keys_str_mv AT ionnechita ontheseparabilityofunitarilyinvariantrandomquantumstatestheunbalancedregime
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