Non-closure of Quantum Correlation Matrices and Factorizable Channels that Require Infinite Dimensional Ancilla (With an Appendix by Narutaka Ozawa)

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

Non-closure of Quantum Correlation Matrices and Factorizable Channels that Require Infinite Dimensional Ancilla (With an Appendix by Narutaka Ozawa). / Musat, Magdalena; Rørdam, Mikael.

In: Communications in Mathematical Physics, Vol. 375, No. 3, 2020, p. 1761-1776.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Musat, M & Rørdam, M 2020, 'Non-closure of Quantum Correlation Matrices and Factorizable Channels that Require Infinite Dimensional Ancilla (With an Appendix by Narutaka Ozawa)', Communications in Mathematical Physics, vol. 375, no. 3, pp. 1761-1776. https://doi.org/10.1007/s00220-019-03449-w

APA

Musat, M., & Rørdam, M. (2020). Non-closure of Quantum Correlation Matrices and Factorizable Channels that Require Infinite Dimensional Ancilla (With an Appendix by Narutaka Ozawa). Communications in Mathematical Physics, 375(3), 1761-1776. https://doi.org/10.1007/s00220-019-03449-w

Vancouver

Musat M, Rørdam M. Non-closure of Quantum Correlation Matrices and Factorizable Channels that Require Infinite Dimensional Ancilla (With an Appendix by Narutaka Ozawa). Communications in Mathematical Physics. 2020;375(3): 1761-1776. https://doi.org/10.1007/s00220-019-03449-w

Author

Musat, Magdalena ; Rørdam, Mikael. / Non-closure of Quantum Correlation Matrices and Factorizable Channels that Require Infinite Dimensional Ancilla (With an Appendix by Narutaka Ozawa). In: Communications in Mathematical Physics. 2020 ; Vol. 375, No. 3. pp. 1761-1776.

Bibtex

@article{71d10ac5f69c4ef1b515390b744122e2,
title = "Non-closure of Quantum Correlation Matrices and Factorizable Channels that Require Infinite Dimensional Ancilla (With an Appendix by Narutaka Ozawa)",
abstract = " We show that there exist factorizable quantum channels in each dimension ≥ 11 which do not admit a factorization through any finite dimensional von Neumann algebra, and do require ancillas of type II 1 , thus witnessing new infinite-dimensional phenomena in quantum information theory. We show that the set of n× n matrices of correlations arising as second-order moments of projections in finite dimensional von Neumann algebras with a distinguished trace is non-closed, for all n≥ 5 , and we use this to give a simplified proof of the recent result of Dykema, Paulsen and Prakash that the set of synchronous quantum correlations Cqs(5,2) is non-closed. Using a trick originating in work of Regev, Slofstra and Vidick, we further show that the set of correlation matrices arising from second-order moments of unitaries in finite dimensional von Neumann algebras with a distinguished trace is non-closed in each dimension ≥ 11 , from which we derive the first result above. ",
author = "Magdalena Musat and Mikael R{\o}rdam",
year = "2020",
doi = "10.1007/s00220-019-03449-w",
language = "English",
volume = "375",
pages = " 1761--1776",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer",
number = "3",

}

RIS

TY - JOUR

T1 - Non-closure of Quantum Correlation Matrices and Factorizable Channels that Require Infinite Dimensional Ancilla (With an Appendix by Narutaka Ozawa)

AU - Musat, Magdalena

AU - Rørdam, Mikael

PY - 2020

Y1 - 2020

N2 - We show that there exist factorizable quantum channels in each dimension ≥ 11 which do not admit a factorization through any finite dimensional von Neumann algebra, and do require ancillas of type II 1 , thus witnessing new infinite-dimensional phenomena in quantum information theory. We show that the set of n× n matrices of correlations arising as second-order moments of projections in finite dimensional von Neumann algebras with a distinguished trace is non-closed, for all n≥ 5 , and we use this to give a simplified proof of the recent result of Dykema, Paulsen and Prakash that the set of synchronous quantum correlations Cqs(5,2) is non-closed. Using a trick originating in work of Regev, Slofstra and Vidick, we further show that the set of correlation matrices arising from second-order moments of unitaries in finite dimensional von Neumann algebras with a distinguished trace is non-closed in each dimension ≥ 11 , from which we derive the first result above.

AB - We show that there exist factorizable quantum channels in each dimension ≥ 11 which do not admit a factorization through any finite dimensional von Neumann algebra, and do require ancillas of type II 1 , thus witnessing new infinite-dimensional phenomena in quantum information theory. We show that the set of n× n matrices of correlations arising as second-order moments of projections in finite dimensional von Neumann algebras with a distinguished trace is non-closed, for all n≥ 5 , and we use this to give a simplified proof of the recent result of Dykema, Paulsen and Prakash that the set of synchronous quantum correlations Cqs(5,2) is non-closed. Using a trick originating in work of Regev, Slofstra and Vidick, we further show that the set of correlation matrices arising from second-order moments of unitaries in finite dimensional von Neumann algebras with a distinguished trace is non-closed in each dimension ≥ 11 , from which we derive the first result above.

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U2 - 10.1007/s00220-019-03449-w

DO - 10.1007/s00220-019-03449-w

M3 - Journal article

AN - SCOPUS:85065142457

VL - 375

SP - 1761

EP - 1776

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -

ID: 223821779