Disproving the conjecture on structural physical approximation to optimal decomposable entanglement witnesses

Abstract

We disprove the conjecture that structural physical approximations to optimal entanglement witnesses are separable states. The conjecture holds true for extremal decomposable entanglement witnesses.

3 pages; minor changes

References in corpus (7)

• Review of Entangled Coherent States
• Entanglement witnesses: construction, analysis and classification
• The information-theoretic costs of simulating quantum measurements
• Structural approximations to positive maps and entanglement breaking channels
• The geometry of bipartite qutrits including bound entanglement
• Exposed positive maps: a sufficient condition
• The structural physical approximations and optimal entanglement witnesses

Cited by in corpus (8)

• Entanglement witnesses: construction, analysis and classification
• Entanglement witnesses from mutually unbiased bases
• Sufficient separability criteria and linear maps
• Checking the optimality of entanglement witnesses: an application to structural physical approximations
• On the structure of mirrored operators obtained from optimal entanglement witnesses
• Linear maps as sufficient criteria for entanglement depth and compatibility in many-body systems
• Extremal entanglement witnesses
• Guaranteeing Completely Positive Quantum Evolution