Resource Theory of Entanglement with a Unique Multipartite Maximally Entangled State

Patricia Contreras-Tejada, Carlos Palazuelos, and Julio I. de Vicente
Phys. Rev. Lett. 122, 120503 – Published 28 March 2019
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Abstract

Entanglement theory is formulated as a quantum resource theory in which the free operations are local operations and classical communication (LOCC). This defines a partial order among bipartite pure states that makes it possible to identify a maximally entangled state, which turns out to be the most relevant state in applications. However, the situation changes drastically in the multipartite regime. Not only do there exist inequivalent forms of entanglement forbidding the existence of a unique maximally entangled state, but recent results have shown that LOCC induces a trivial ordering: almost all pure entangled multipartite states are incomparable (i.e., LOCC transformations among them are almost never possible). In order to cope with this problem we consider alternative resource theories in which we relax the class of LOCC to operations that do not create entanglement. We consider two possible theories depending on whether resources correspond to multipartite entangled or genuinely multipartite entangled (GME) states and we show that they are both nontrivial: no inequivalent forms of entanglement exist in them and they induce a meaningful partial order (i.e., every pure state is transformable to more weakly entangled pure states). Moreover, we prove that the resource theory of GME that we formulate here has a unique maximally entangled state, the generalized GHZ state, which can be transformed to any other state by the allowed free operations.

  • Received 4 September 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.120503

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Patricia Contreras-Tejada1, Carlos Palazuelos2,1, and Julio I. de Vicente3

  • 1Instituto de Ciencias Matemáticas, E-28049 Madrid, Spain
  • 2Departamento de Análisis Matemático y Matemática Aplicada, Universidad Complutense de Madrid, E-28040 Madrid, Spain
  • 3Departamento de Matemáticas, Universidad Carlos III de Madrid, E-28911 Leganés (Madrid), Spain

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Issue

Vol. 122, Iss. 12 — 29 March 2019

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