Perturbative expansion of entanglement negativity using patterned matrix calculus

Jesse C. Cresswell, Ilan Tzitrin, and Aaron Z. Goldberg
Phys. Rev. A 99, 012322 – Published 14 January 2019

Abstract

Negativity is an entanglement monotone frequently used to quantify entanglement in bipartite states. Because negativity is a nonanalytic function of a density matrix, existing methods used in the physics literature are insufficient to compute its derivatives. To this end we develop techniques in the calculus of complex, patterned matrices and use them to conduct a perturbative analysis of negativity in terms of arbitrary variations of the density operator. The result is an easy-to-implement expansion that can be carried out to all orders. On the way we provide convenient representations of the partial transposition map appearing in the definition of negativity. Our methods are well suited to study the growth and decay of entanglement in a wide range of physical systems, including the generic linear growth of entanglement in many-body systems, and have broad relevance to many functions of quantum states and observables.

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  • Received 21 September 2018
  • Corrected 25 April 2019

DOI:https://doi.org/10.1103/PhysRevA.99.012322

©2019 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Corrections

25 April 2019

Correction: A misrepresentation of Eq. (D2) introduced during the production cycle has been fixed.

Authors & Affiliations

Jesse C. Cresswell*, Ilan Tzitrin, and Aaron Z. Goldberg

  • Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada

  • *jcresswe@physics.utoronto.ca
  • itzitrin@physics.utoronto.ca
  • goldberg@physics.utoronto.ca

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Issue

Vol. 99, Iss. 1 — January 2019

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