Gaussian entanglement witness and refined Werner-Wolf criterion for continuous variables

Xiao-yu Chen, Maoke Miao, Rui Yin, and Jiantao Yuan
Phys. Rev. A 107, 022410 – Published 8 February 2023

Abstract

We use matched quantum entanglement witnesses to study the separable criteria of continuous variable states. The witness can be written as an identity operator minus a Gaussian operator. The optimization of the witness then is transformed to an eigenvalue problem of a Gaussian kernel integral equation. It follows a separable criterion not only for symmetric Gaussian quantum states, but also for non-Gaussian states prepared by photon adding to and/or subtracting from symmetric Gaussian states. Based on Fock space numeric calculation, we obtain an entanglement witness for more general two-mode states. A necessary criterion of separability follows for two-mode states and it is shown to be necessary and sufficient for a two-mode squeezed thermal state and the related two-mode non-Gaussian states. We also connect the witness-based criterion with Werner-Wolf criterion and refine the Werner-Wolf criterion.

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  • Received 16 February 2022
  • Revised 11 December 2022
  • Accepted 9 January 2023

DOI:https://doi.org/10.1103/PhysRevA.107.022410

©2023 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Xiao-yu Chen, Maoke Miao, Rui Yin, and Jiantao Yuan

  • School of Information and Electrical Engineering, Zhejiang University City College, Hangzhou 310015, China

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Issue

Vol. 107, Iss. 2 — February 2023

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