• Open Access

Exponentially many entanglement and correlation constraints for multipartite quantum states

Christopher Eltschka, Felix Huber, Otfried Gühne, and Jens Siewert
Phys. Rev. A 98, 052317 – Published 14 November 2018

Abstract

We present a family of correlation constraints that apply to all multipartite quantum systems of finite dimension. The size of this family is exponential in the number of subsystems. We obtain these relations by defining and investigating the generalized state inversion map. This map provides a systematic way to obtain local unitary invariants of degree two in the state and is directly linked to the shadow inequalities proved by Rains [IEEE Trans. Inf. Theory 46, 54 (2000)]. The constraints are stated in terms of linear inequalities for the linear entropies of the subsystems. For pure quantum states they turn into monogamy relations that constrain the distribution of bipartite entanglement among the subsystems of the global state.

  • Received 2 August 2018

DOI:https://doi.org/10.1103/PhysRevA.98.052317

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

©2018 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Christopher Eltschka1, Felix Huber2,3,4, Otfried Gühne4, and Jens Siewert5,6

  • 1Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
  • 2ICFO–Institut de Ciències Fotòniques, Barcelona Institute of Science and Technology, E-08860 Castelldefels (Barcelona), Spain
  • 3Institut für Theoretische Physik, Universität zu Köln, D-50937 Köln, Germany
  • 4Naturwissenschaftlich-Technische Fakultät, Universität Siegen, D-57068 Siegen, Germany
  • 5Departamento de Química Física, Universidad del País Vasco UPV/EHU, E-48080 Bilbao, Spain
  • 6IKERBASQUE Basque Foundation for Science, E-48013 Bilbao, Spain

Article Text

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Issue

Vol. 98, Iss. 5 — November 2018

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