Inseparability inequalities for higher-order moments for bipartite systems

Abstract

There are several examples of bipartite entangled states of continuous variables for which the existing criteria for entanglement using the inequalities involving the second order moments are insufficient. We derive new inequalities involving higher order correlation, for testing entanglement in non-Gaussian states. In this context we study an example of a non-Gaussian state, which is a bipartite entangled state of the form $\psi (x_{\mathrm{a}},x_{\mathrm{b}})\propto (\alpha x_{\mathrm{a}}+\beta x_{\mathrm{b}})e^{-(x_{\mathrm{a}}^2+x_{\mathrm{b}}^2)/2}$. Our results open up an avenue to search for new inequalities to test entanglement in non-Gaussian states.

7 pages, Submitted

References in corpus (2)

• Nonclassicality of a photon-subtracted Gaussian field
• Loophole-free test of quantum non-locality using high-efficiency homodyne detectors

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