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.
Bound entangled Gaussian states
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abstract
We discuss the entanglement properties of bipartite states with Gaussian Wigner functions. Separability and the positivity of the partial transpose are characterized in terms of the covariance matrix of the state, and it is shown that for systems composed of a single oscillator for Alice and an arbitrary number for Bob, positivity of the partial transpose implies separability. However, this implications fails with two oscillators on each side, as we show by a five parameter family of explicit counterexamples.
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Numerical evidence from projections and witnesses on specific Gaussian families leads to the conjecture that full inseparability implies genuine multipartite entanglement for all Gaussian states.
citing papers explorer
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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.
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On the existence of fully inseparable biseparable Gaussian states
Numerical evidence from projections and witnesses on specific Gaussian families leads to the conjecture that full inseparability implies genuine multipartite entanglement for all Gaussian states.