Peres-Horodecki Separability Criterion for Continuous Variable Systems

1999/09/14 by R. Simon · 13 citations
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum optics and atomic interactions #quant-ph

paper · pdf · doi:10.1103/physrevlett.84.2726

6 pages, no figures

arxiv created 1999/09/14 · openalex publication_date 2000/03/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

The Peres-Horodecki criterion of positivity under partial transpose is studied in the context of separability of bipartite continuous variable states. The partial transpose operation admits, in the continuous case, a geometric interpretation as mirror reflection in phase space. This recognition leads to uncertainty principles, stronger than the traditional ones, to be obeyed by all separable states. For all bipartite Gaussian states, the Peres-Horodecki criterion turns out to be a necessary and sufficient condition for separability.

Citations

• Teleportation of quantum states
• Separability Criterion for Density Matrices
• Unconditional Quantum Teleportation
• Inseparability Criterion for Continuous Variable Systems
• Teleportation of Continuous Quantum Variables
• On the Quantum Correction For Thermodynamic Equilibrium
• Quantum Computation

Cited by

• Bound Entangled Gaussian States
• Inseparability Criteria for Continuous Bipartite Quantum States
• Entropic Entanglement Criteria for Continuous Variables
• Generalized concurrence measure for faithful quantification of multiparticle pure state entanglement using Lagrange’s identity and wedge product
• Generalized entanglement measure for continuous-variable systems
• Direct observation of deterministic macroscopic entanglement
• Entanglement criteria via concave-function uncertainty relations
• Route to ponderomotive entanglement of light via optically trapped mirrors
• Emergence of Gaussian entanglement and non-Gaussianity in high-harmonic generation driven by bright squeezed light
• On the existence of fully inseparable biseparable Gaussian states
• Non-Gaussian Entanglement Hierarchy Based on the Schmidt Number
• The uncertainty geometry of finite-dimensional position and momentum
• Quantum entanglement [wikipedia]