A class of positive atomic maps

2007/11/28 by Dariusz Chruściński, Dariusz Chruscinski, Andrzej Kossakowski · 23 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebra over a field #Class (philosophy) #Computer science #Construct (python library) #Epistemology #Indecomposable module #Mathematics #Philosophy #Physics #Property (philosophy) #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Theoretical physics #math-ph #math.MP #math.OA #quant-ph

paper · pdf · doi:10.1088/1751-8113/41/21/215201

published in Journal of Physics A Mathematical and Theoretical 41(21), 215201 (Institute of Physics) · 15 pages

arxiv created 2007/11/28 · openalex publication_date 2008/05/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We construct a new class of positive indecomposable maps in the algebra of d × d complex matrices. These maps are characterized by the ‘weakest’ positivity property and for this reason they are called atomic. This class provides a new rich family of atomic entanglement witnesses which define an important tool for investigating quantum entanglement. It turns out that they are able to detect states with the ‘weakest’ quantum entanglement.

Citations

• Class of bound entangled states ofN+Nqubits revealed by nondecomposable maps
• Optimal Entanglement Criterion for Mixed Quantum States
• Entanglement in SO(3)-invariant bipartite quantum systems
• State space structure and entanglement of rotationally invariant spin systems
• Schmidt number for density matrices
• Separability Criterion for Density Matrices
• Optimization of entanglement witnesses
• Construction of entangled states with positive partial transposes based on indecomposable positive linear maps
• Completely positive linear maps on complex matrices
• Separability of mixed states: necessary and sufficient conditions
• Subalgebras of C*-algebras
• Positive linear maps of operator algebras

Cited by

• Entanglement witnesses: construction, analysis and classification
• How to construct indecomposable entanglement witnesses