Constructing optimal entanglement witnesses. II

Abstract

We provide a class of optimal nondecomposable entanglement witnesses for 4N x 4N composite quantum systems or, equivalently, a new construction of nondecomposable positive maps in the algebra of 4N x 4N complex matrices. This construction provides natural generalization of the Robertson map. It is shown that their structural physical approximations give rise to entanglement breaking channels.

6 pages

References in corpus (7)

• 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
• Spectral conditions for positive maps
• A class of positive atomic maps

Cited by in corpus (26)

• Entanglement witnesses: construction, analysis and classification
• One parameter family of indecomposable optimal entanglement witnesses arising from generalized Choi maps
• Optimal entanglement witnesses from generalized reduction and Robertson maps
• On structural physical approximations and entanglement breaking maps
• Designing Quantum Information Processing via Structural Physical Approximation
• Complete Entanglement Witness for Quantum Teleportation
• A class of exposed indecomposable positive maps
• The structural physical approximations and optimal entanglement witnesses
• Sufficient separability criteria and linear maps
• Structural physical approximations and entanglement witnesses
• Inertias of entanglement witnesses
• Checking the optimality of entanglement witnesses: an application to structural physical approximations
• Disproving the conjecture on structural physical approximation to optimal decomposable entanglement witnesses
• A class of Bell diagonal entanglement witnesses in ${\mathbb{C}}^4\otimes {\mathbb{C}}^4$: optimization and the spanning property
• The hierarchies of "witnesses" and the properties and characterization of entangled states as super entanglement witnesses
• Entangled states in the role of witnesses
• Inequalities detecting entanglement for arbitrary bipartite systems
• New tools for investigating positive maps in matrix algebras
• Constructing all entanglement witnesses from density matrices
• Entanglement witnesses for $d\otimes d$ systems and new classes of entangled qudit states
• Recurrent construction of optimal entanglement witnesses for 2N qubit systems
• A characterization of entangled two-qubit states via partial-transpose-moments
• Entanglement detection and lower bound of convex-roof extension of negativity
• Linear maps as sufficient criteria for entanglement depth and compatibility in many-body systems
• Universal methods for extending any entanglement witness from the bipartite to the multipartite case
• Guaranteeing Completely Positive Quantum Evolution