Optimal indecomposable witnesses without extremality or the spanning property

2012/06/04 by Kil-Chan Ha, Hoseog Yu · 1 citation
Mathematics · Physics and Astronomy · #Basis (linear algebra) #Existential quantification #Indecomposable module #Numerical methods in inverse problems #Property (philosophy) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #Witness #math-ph #math.MP #math.OA #msc:15A30 #msc:15A90 #msc:46L05 #msc:81P15 #msc:94A15 #quant-ph

paper · pdf · doi:10.1088/1751-8113/45/39/395307

published as Journal of Physics A: Mathematical and General, 45 (2012), 395307 · 17 pages

arxiv created 2012/06/04 · openalex publication_date 2012/09/13 · arxiv updated 2015/06/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

Abstract

One of the interesting problems of optimal indecomposable entanglement witnesses is whether there exists an optimal indecomposable entanglement witness which neither has the spanning property nor is associated with an extremal positive linear map. Here, we answer this question in the negative by examining the extremality of the positive linear maps constructed by Qi and Hou (2011 J. Phys. A: Math. Theor. 44 215305).

Citations

• Entanglement Witnesses Arising from Exposed Positive Linear Maps
• 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

Cited by

• Extremal extensions of entanglement witnesses and their connection with unextendable product bases