A family of nonlocal bound entangled states

TL;DR

This paper constructs a broad family of nonlocal bound entangled states for all finite dimensions above two, demonstrating their nonlocality through Bell and steering inequalities, and providing tools for their detection.

Contribution

It extends the construction of nonlocal bound entangled states to all higher dimensions and introduces new inequalities and witnesses for their identification.

Findings

Constructed nonlocal bound entangled states for all finite dimensions > 2.

Proposed a Hardy-type Bell inequality and a steering inequality for these states.

Provided entanglement witnesses to detect their entanglement beyond Bell and steering tests.

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.