Generic Entanglement and Standard Form for N-mode Pure Gaussian States

Abstract

We investigate the correlation structure of pure N-mode Gaussian resources which can be experimentally generated by means of squeezers and beam splitters, whose entanglement properties are generic. We show that those states are specified (up to local unitaries) by N(N-1)/2 parameters, corresponding to the two-point correlations between any pair of modes. Our construction yields a practical scheme to engineer such generic-entangled N-mode pure Gaussian states by linear optics. We discuss our findings in the framework of Gaussian matrix product states of harmonic lattices, raising connections with entanglement frustration and the entropic area law.

4 pages, 1 EPS figure. Revised, corrected and clarified. Final shortened version, published in PRL

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Cited by in corpus (6)

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• Building Gaussian Cluster States by Linear Optics
• Optical state engineering, quantum communication, and robustness of entanglement promiscuity in three-mode Gaussian states
• Not-so-normal mode decomposition
• Standard forms and entanglement engineering of multimode Gaussian states under local operations
• Geometric characterization of separability and entanglement in pure Gaussian states by single-mode unitary operations