arXiv:2209.08746 · Physical Review A

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

Xiaoyu Chen, Maoke Miao, Rui Yin, Jiantao Yuan

Published Feb 8, 2023• 6 citations

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.

DOI: 10.1103/physreva.107.022410

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