Disproving the Peres conjecture: Bell nonlocality from bipartite bound entanglement

TL;DR

This paper disproves the Peres conjecture by demonstrating that bound entangled states, which are undistillable, can still violate Bell inequalities, revealing a more complex relationship between entanglement and nonlocality.

Contribution

It provides the first explicit example of a bound entangled state violating a Bell inequality, challenging previous assumptions about entanglement and nonlocality.

Findings

Bound entangled states can violate Bell inequalities.

Bell nonlocality does not imply entanglement distillability.

Bound entanglement can be used for device-independent randomness certification.

Abstract

Quantum entanglement plays a central role in many areas of physics, from quantum information science to many-body systems. In order to grasp the essence of this phenomenon, it is fundamental to understand how different manifestations of entanglement relate to each other. In 1999, Peres conjectured that Bell nonlocality is equivalent to distillability of entanglement. The intuition of Peres was that the non-classicality of an entangled state, as witnessed via Bell inequality violation, implies that pure entanglement can be distilled from this state, hence making it useful for most quantum information protocols. Subsequently, the Peres conjecture was shown to hold true in several specific cases, and became a central open question in quantum information theory. Here we disprove the Peres conjecture by showing that an undistillable bipartite entangled state---a bound entangled state---can nevertheless violate a Bell inequality. This shows that Bell nonlocality implies neither entanglement distillability, nor non-positivity under partial transposition, thus clarifying the relation between three fundamental aspects of entanglement. Finally, our results lead to a novel application of bound entanglement for device-independent randomness certification.