A Family of Continuous Variable Entanglement Criteria using General Entropy Functions

Abstract

We derive a family of entanglement criteria for continuous variable systems based on the Rényi entropy of complementary distributions. We show that these entanglement witnesses can be more sensitive than those based on second-order moments, as well as previous tests involving the Shannon entropy [Phys. Rev. Lett. \textbf{103}, 160505 (2009)]. We extend our results to include the case of discrete sampling, and develop another set of entanglement tests using the discrete Tsallis entropy. We provide several numerical results which show that our criteria can be used to identify entanglement in a number of experimentally relevant quantum states.

8 pages, 3 figures

References in corpus (17)

• Entanglement detection
• Entanglement in continuous variable systems: Recent advances and current perspectives
• Formulation of the uncertainty relations in terms of the Renyi entropies
• Experimental entanglement distillation of mesoscopic quantum states
• Multimode uncertainty relations and separability of continuous variable states
• Entanglement conditions for two-mode states: Applications
• Entropic Entanglement Criteria for Continuous Variables
• Necessary and sufficient conditions for bipartite entanglement
• Preparation of distilled and purified continuous variable entangled states
• Inseparability criteria based on matrices of moments
• Uncertainty inequalities as entanglement criteria for negative partial-transpose states
• Detecting entanglement with non-hermitian operators
• Iterations of nonlinear entanglement witnesses
• Operational Quantification of Continuous Variable Correlations
• Experimentally friendly bounds on non-Gaussian entanglement from second moments
• Separability criteria for continuous variable systems
• Generalized squeezing operators, bipartite Wigner functions and entanglement via Wehrl's entropy functionals

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