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.
- Received 16 February 2022
- Revised 11 December 2022
- Accepted 9 January 2023
DOI:https://doi.org/10.1103/PhysRevA.107.022410
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