Optimal entanglement witnesses from generalized reduction and Robertson maps

Abstract

We provide a generalization of the reduction and Robertson positive maps in matrix algebras. They give rise to a new class of optimal entanglement witnesses. Their structural physical approximation is analyzed. As a byproduct we provide a new examples of PPT (Positive Partial Transpose) entangled states.

14 pages

References in corpus (10)

• Entanglement detection
• Detecting Genuine Multipartite Entanglement with Two Local Measurements
• Quantifying Entanglement with Witness Operators
• Optimal entanglement criterion for mixed quantum states
• Structural approximations to positive maps and entanglement breaking channels
• Separable Multipartite Mixed States - Operational Asymptotically Necessary and Sufficient Conditions
• Spectral conditions for positive maps
• A new class of states with positive partial transposition
• Constructing optimal entanglement witnesses. II
• A class of positive atomic maps

Cited by in corpus (17)

• Entanglement witnesses: construction, analysis and classification
• One parameter family of indecomposable optimal entanglement witnesses arising from generalized Choi maps
• Optimal decomposable witnesses without the spanning property
• Designing Quantum Information Processing via Structural Physical Approximation
• Exposed positive maps: a sufficient condition
• A class of exposed indecomposable positive maps
• The structural physical approximations and optimal entanglement witnesses
• Entanglement witnesses arising from Choi type positive linear maps
• Checking the optimality of entanglement witnesses: an application to structural physical approximations
• A class of Bell diagonal entanglement witnesses in ${\mathbb{C}}^4\otimes {\mathbb{C}}^4$: optimization and the spanning property
• Construction of optimal teleportation witness operators from entanglement witnesses
• New tools for investigating positive maps in matrix algebras
• On the structure of mirrored operators obtained from optimal entanglement witnesses
• Recurrent construction of optimal entanglement witnesses for 2N qubit systems
• A class of generalized positive linear maps on matrix algebras
• Guaranteeing Completely Positive Quantum Evolution
• Constructing positive maps from block matrices