A single-copy homodyne protocol estimates unbiased U-statistics for partial-transpose moments p2 and p3 to detect bipartite CV entanglement, with sample complexity O((N+1)^{14/3}/ε²) and demonstrations on six state families.
Inseparability criterion for continuous variable systems
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abstract
An inseparability criterion based on the total variance of a pair of Einstein-Podolsky-Rosen type operators is proposed for continuous variable systems. The criterion provides a sufficient condition for entanglement of any two-party continuous variable states. Furthermore, for all the Gaussian states, this criterion turns out to be a necessary and sufficient condition for inseparability.
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Covariance matrices for finite-dimensional DFT-related position-momentum pairs are fully characterized via unitary invariants, convex geometry, and SDP, yielding extremal states and application bounds.
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Detecting entanglement of non-Gaussian continuous-variable states from single-copy homodyne measurements
A single-copy homodyne protocol estimates unbiased U-statistics for partial-transpose moments p2 and p3 to detect bipartite CV entanglement, with sample complexity O((N+1)^{14/3}/ε²) and demonstrations on six state families.
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The uncertainty geometry of finite-dimensional position and momentum
Covariance matrices for finite-dimensional DFT-related position-momentum pairs are fully characterized via unitary invariants, convex geometry, and SDP, yielding extremal states and application bounds.