Entanglement negativity bounds for fermionic Gaussian states

Jens Eisert, Viktor Eisler, Z. Zimborás

Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

Abstract

The entanglement negativity is a versatile measure of entanglement that has numerous applications in quantum information and in condensed matter theory. It can not only efficiently be computed in the Hilbert space dimension, but for non-interacting bosonic systems, one can compute the negativity efficiently in the number of modes. However, such an efficient computation does not carry over to the fermionic realm, the ultimate reason for this being that the partial transpose of a fermionic Gaussian state is no longer Gaussian. To provide a remedy for this state of affairs, in this work we introduce efficiently computable and rigorous upper and lower bounds to the negativity, making use of techniques of semi-definite programming, building upon the Lagrangian formulation of fermionic linear optics, and exploiting suitable products of Gaussian operators. We discuss examples in quantum many-body theory and hint at applications in the study of topological properties at finite temperature.
Originalspracheenglisch
Aufsatznummer165123
Seitenumfang12
FachzeitschriftPhysical Review / B
Jahrgang97
Ausgabenummer16
DOIs
PublikationsstatusVeröffentlicht - 13 Apr 2018

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Hilbert space
programming
optics
formulations
operators
products
temperature

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    Entanglement negativity bounds for fermionic Gaussian states. / Eisert, Jens; Eisler, Viktor; Zimborás, Z.

    in: Physical Review / B, Jahrgang 97, Nr. 16, 165123, 13.04.2018.

    Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

    Eisert, Jens ; Eisler, Viktor ; Zimborás, Z. / Entanglement negativity bounds for fermionic Gaussian states. in: Physical Review / B. 2018 ; Jahrgang 97, Nr. 16.
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