Construction of noisy bound entangled states and the range criterion

Abstract

In this work we consider bipartite noisy bound entangled states with positive partial transpose, that is, such a state can be written as a convex combination of an edge state and a separable state. In particular, we present schemes to construct distinct classes of noisy bound entangled states which satisfy the range criterion. As a consequence of the present study we also identify noisy bound entangled states which do not satisfy the range criterion. All of the present states are constituted by exploring different types of product bases.

Close to published version

References in corpus (9)

• Entanglement detection
• Covariance matrices and the separability problem
• Disproving the Peres conjecture: Bell nonlocality from bipartite bound entanglement
• Steering bound entangled states: A counterexample to the stronger Peres conjecture
• Quantum states with a positive partial transpose are useful for metrology
• Family of bound entangled states on the boundary of Peres set
• Bound entangled states fit for robust experimental verification
• A simple class of bound entangled states based on the properties of the antisymmetric subspace
• Robustness of entangled states that are positive under partial transposition

Cited by in corpus (13)

• Strong quantum nonlocality for unextendible product bases in heterogeneous systems
• Distinguishability classes, resource sharing, and bound entanglement distribution
• Unextendible product bases, bound entangled states, and the range criterion
• Nonlocality of tripartite orthogonal product states
• Separability and entanglement in superpositions of quantum states
• Increasing distillable key rate from bound entangled states by using local filtration
• Witness Operator Provides Better Estimate of the Lower Bound of Concurrence of Bipartite Bound Entangled States in $d_1\otimes d_2$ Dimensional System
• Construction of PPT entangled state and its detection by using second-order moment of the partial transposition
• Useful variants and perturbations of completely entangled subspaces and spans of unextendible product bases
• Practical construction of positive maps which are not completely positive
• Bound entanglement in symmetric random induced states
• Enhanced separability criteria based on symmetric measurements
• Quantum Separability Criteria Based on Symmetric Measurements