Separability Criterion for Gaussian States

Alexandr Sergeevich, Vladimir I. Man’ko

Krzysztof Wódkiewicz, Berthold‐Georg Englert

K. V. S. Shiv Chaitanya, Sibasish Ghosh A, Venkatraman Srinivasan

In this paper, we give Separability criterion for the multi-mode Gaussian states using the Marchenko-Pastur theorem. We show that the Marchenko-Pastur theorem from random matrix theory as necessary and sufficient condition for separability of multimode Gaussian states.

Derek McHugh, Vladimír Bužek, Mário Ziman

We present a class of non-Gaussian two-mode continuous-variable states for which the separability criterion for Gaussian states can be employed to detect whether they are separable or not. These states reduce to the two-mode Gaussian states as a special case.

Maurice A. de Gosson

Xiaoyu Chen, Maoke Miao, Rui Yin +1 more

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.