Determination of the Schmidt number

Abstract

Optimized, necessary and sufficient conditions for the identification of the Schmidt number will be derived in terms of general Hermitian operators. These conditions apply to arbitrary mixed quantum states. The optimization procedure delivers equations similar to the eigenvalue problem of an operator. The properties of the solution of these equations will be studied. We solve these equations for classes of operators. The solutions will be applied to phase randomized two-mode squeezed-vacuum states in continuous variable systems.

12 pages, 3 figures, PRA in press, previously: Section IV in arXiv:0908.3974v2

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• Measurement-Device-Independent Approach to Entanglement Measures
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• Fidelity matters: the birth of entanglement in the interference of Gaussian states
• Entanglement in macroscopic systems
• Design and Experimental Performance of Local Entanglement Witness Operators
• Strongly entangled light from planar microcavities
• Numerical construction of multipartite entanglement witnesses
• Experimental hierarchy of two-qubit quantum correlations without state tomography
• Multipartite entangled light from driven microcavities
• Operational Gaussian Schmidt-Number Witnesses
• Norms and Cones in the Theory of Quantum Entanglement
• Entanglement verification of noisy N00N states
• Construction of optimal teleportation witness operators from entanglement witnesses
• Bipartite bound entanglement in continuous variables through deGaussification
• Schmidt-number benchmarks for continuous-variable quantum devices
• The Schmidt number and partially entanglement breaking channels in infinite dimensions
• Simulating quantum instruments with projective measurements and quantum post-processing
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• Entangled light from driven dissipative microcavities
• Generation, dynamical buildup and detection of bi- and mulipartite entangled states in cavity systems