A family of nonlocal bound entangled states

Abstract

Bound entanglement, being entangled yet not distillable, is essential to our understandings of the relations between nonlocality and entanglement besides its applications in certain quantum information tasks. Recently, bound entangled states that violate a Bell inequality have been constructed for a two-qutrit system, disproving a conjecture by Peres that bound entanglement is local. Here we shall construct such kind of nonlocal bound entangled states for all finite dimensions larger than two, making possible their experimental demonstrations on most general systems. We propose a Bell inequality, based on a Hardy-type argument for nonlocality, and a steering inequality to identify their nonlocality. We also provide a family of entanglement witnesses to detect their entanglement beyond the Bell inequality and the steering inequality.

9 Pages, 2 Tables + 3 Figures

References in corpus (6)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Entanglement witnesses: construction, analysis and classification
• Disproving the Peres conjecture: Bell nonlocality from bipartite bound entanglement
• Steering bound entangled states: A counterexample to the stronger Peres conjecture
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Cited by in corpus (19)

• Quantum Steering
• Steering criteria from general entropic uncertainty relations
• Bound entanglement from randomized measurements
• Family of bound entangled states on the boundary of Peres set
• Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems
• Pearson Correlation Coefficient as a measure for Certifying and Quantifying High Dimensional Entanglement
• Distinguishability classes, resource sharing, and bound entanglement distribution
• Construction of noisy bound entangled states and the range criterion
• Bound entangled singlet-like states for quantum metrology
• Quantum measurement incompatibility in subspaces
• Unextendible product bases, bound entangled states, and the range criterion
• Family of Bell inequalities violated by higher-dimensional bound entangled states
• A class of genuinely high-dimensionally entangled states with a positive partial transpose
• Characterizing generalized axisymmetric quantum states in $d\times d$ systems
• Bound entangled states are useful in prepare-and-measure scenarios
• Demonstration of monogamy laws for Gaussian steering in optomechanics
• Investigating bound entangled two-qutrit states via the best separable approximation
• Bound entanglement-assisted prepare-and-measure scenarios based on four-dimensional quantum messages
• Unlimited quantum correlation advantage from bound entanglement