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

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

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

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*Communications in Mathematical Physics*, vol. 375, no. 3, pp. 1761-1776. https://doi.org/10.1007/s00220-019-03449-w

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*Communications in Mathematical Physics*,

*375*(3), 1761-1776. https://doi.org/10.1007/s00220-019-03449-w

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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.

UR - http://www.scopus.com/inward/record.url?scp=85065142457&partnerID=8YFLogxK

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