Rényi formulation of entanglement criteria for continuous variables

Alexey E. Rastegin
Phys. Rev. A 95, 042334 – Published 21 April 2017

Abstract

Entanglement criteria for an n-partite quantum system with continuous variables are formulated in terms of Rényi entropies. Rényi entropies are widely used as a good information measure due to many nice properties. Derived entanglement criteria are based on several mathematical results such as the Hausdorff-Young inequality, Young's inequality for convolution and its converse. From the historical viewpoint, the formulations of these results with sharp constants were obtained comparatively recently. Using the position and momentum observables of subsystems, one can build two total-system measurements with the following property. For product states, the final density in each global measurement appears as a convolution of n local densities. Hence, restrictions in terms of two Rényi entropies with constrained entropic indices are formulated for n-separable states of an n-partite quantum system with continuous variables. Experimental results are typically sampled into bins between prescribed discrete points. For these aims, we give appropriate reformulations of the derived entanglement criteria.

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  • Received 1 December 2016

DOI:https://doi.org/10.1103/PhysRevA.95.042334

©2017 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Alexey E. Rastegin

  • Department of Theoretical Physics, Irkutsk State University, Gagarin Bv. 20, Irkutsk 664003, Russia

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Issue

Vol. 95, Iss. 4 — April 2017

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