Continuous optimal ensembles I: A geometrical characterization of robustly separable quantum states

2005/03/21 by Romàn R. Zapatrin, Roman R. Zapatrin, Zapatrin, Roman R. · 3 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Quantum optics and atomic interactions #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/0503173

arxiv created 2005/03/21 · openalex publication_date 2005/03/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A geometrical characterization of robustly separable (that is, remaining separable under sufficiently small variiations) mixed states of a bipartite quantum system is given. It is shown that the density matrix of any such state can be represented as a normal vector to a hypersurface in the Euclidean space of all self-adjoint operators in the state space of the whole system. The expression for this hypersurface is provided.

Citations

• Separability Criterion for Density Matrices

Cited by

• Computing finite-dimensional bipartite quantum separability
• An asymptotical separability criterion for bipartite density operators
• Continuous optimal ensembles II. Reducing the separability condition to numerical equations

Related

• Continuous optimal ensembles II. Reducing the separability condition to numerical equations
• New Invariants and Separability criterion of the Mixed States: Bipartite Case
• Entanglement of Bipartite Gaussian States: a Simple Criterion and its Geometric Interpretation
• Smallest disentangling state spaces for general entangled bipartite quantum states
• Separability criterion for bipartite states and its generalization to multipartite systems