2000/09/28 by Reinhard F. Werner, R. F. Werner, M. M. Wolf +1 · 4 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1103/physrevlett.86.3658
4 pages
arxiv created 2000/09/28 · openalex publication_date 2001/04/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss the entanglement properties of bipartite states with Gaussian Wigner functions. For the separability, and the positivity of the partial transpose, we establish explicit necessary and sufficient criteria in terms of the covariance matrix of the state. 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 implication fails with two oscillators on each side, as we show by constructing a five parameter family of bound entangled Gaussian states.