Optimal Entanglement Criterion for Mixed Quantum States

2006/05/31 by Heinz-Peter Breuer, Heinz‐Peter Breuer · 7 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.97.080501

published as Phys. Rev. Lett. 97, 080501 (2006) · 4 pages, no figures, replaced by published version (minor changes), Journal-reference added

arxiv created 2006/08/22 · openalex publication_date 2006/08/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a strong and computationally simple entanglement criterion. The criterion is based on an elementary positive map Phi which operates on state spaces with even dimension N > or = 4. It is shown that Phi detects many entangled states with a positive partial transposition (PPT) and that it leads to a class of optimal entanglement witnesses. This implies that there are no other witnesses which can detect more entangled PPT states. The map Phi yields a systematic method for the explicit construction of high-dimensional manifolds of bound entangled states.

Citations

• Entanglement in SO(3)-invariant bipartite quantum systems
• State space structure and entanglement of rotationally invariant spin systems
• Entanglement in SU(2)-invariant quantum systems: The positive partial transpose criterion and others
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Distinguishing Separable and Entangled States
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Entanglement of Formation of Bipartite Quantum States
• Separability Criterion for Density Matrices
• Reflections upon separability and distillability
• Concurrence of arbitrary dimensional bipartite quantum states

Cited by

• Maximum entanglement in squeezed boson and fermion states
• Entanglement and Permutational Symmetry
• Beyond the standard entropic inequalities: Stronger scalar separability criteria and their applications
• Separability criteria and bounds for entanglement measures
• General scheme for construction of scalar separability criteria from positive maps
• Inseparability criteria based on matrices of moments
• Unifying several separability conditions using the covariance matrix criterion