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arXiv:1610.03205 · Physical Review A

Correlation-based entanglement criteria for bipartite systems

Yumang Jing, Qiongyi He, Tim Byrnes

Published May 2, 2017• 3 citations
arXivHTMLPDF

Abstract

We introduce a class of inequalities based on low-order correlations of operators to detect entanglement in bipartite systems. The operators may either be Hermitian or non-Hermitian and are applicable to any physical system or class of states. Testing the criteria on example systems reveals that they outperform other common correlation-based criteria, such as those by Duan-Giedke-Cirac-Zoller and Hillery-Zubairy. One unusual feature of the criteria is that the correlations include the density matrix itself, which is related to the purity of the system. We discuss how such a term could be measured in relation to the criteria.

DOI
10.1103/physreva.95.052305

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We introduce a class of inequalities based on low-order correlations of operators to detect entanglement in bipartite systems. The operators may either be Hermitian or non-Hermitian and are applicable to any physical system or class of states. Testing the criteria on example systems reveals that they outperform other common correlation-based criteria, such as those by Duan-Giedke-Cirac-Zoller and Hillery-Zubairy. One unusual feature of the criteria is that the correlations include the density matrix itself, which is related to the purity of the system. We discuss how such a term could be measured in relation to the criteria.
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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 . Our results open up an avenue to search for new inequalities to test entanglement in non-Gaussian states.
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Abstract Quantum entanglement plays a key role in quantum computation and quantum information processing. It is of great significance to find efficient and experimentally friend separability criteria to detect entanglement. In this paper, we firstly propose two easily used entanglement criteria based on matrix moments. The first entanglement criterion only uses the first two realignment moments of a density matrix. The second entanglement criterion is based on the moments related to the partially transposed matrix. By detailed examples we illustrate the effectiveness of these criteria in detecting entanglement. Moreover, we provide an experimentally measurable lower bound of concurrence based on these moments. Finally, we present both bipartite and genuine tripartite entanglement measures based on the moments of the reduced states. By detailed examples, we show that our entanglement measures characterize the quantum entanglement in a more fine ways than the existing measures.