Quantum nonlocality does not imply entanglement distillability

TL;DR

This paper demonstrates that quantum nonlocality can exist without entanglement distillability, providing a counterexample of a bound entangled state that violates Bell inequalities, thus clarifying the complex relationship between nonlocality and entanglement.

Contribution

It constructs a specific 3-qubit bound entangled state that violates Bell inequalities, disproving a longstanding conjecture and showing nonlocality does not imply distillable entanglement.

Findings

A 3-qubit bound entangled state violates Bell inequality

No bipartite entanglement can be distilled from this state

Disproves the multipartite version of Peres' conjecture

Abstract

Entanglement and nonlocality are both fundamental aspects of quantum theory, and play a prominent role in quantum information science. The exact relation between entanglement and nonlocality is however still poorly understood. Here we make progress in this direction by showing that, contrary to what previous work suggested, quantum nonlocality does not imply entanglement distillability. Specifically, we present analytically a 3-qubit entangled state that is separable along any bipartition. This implies that no bipartite entanglement can be distilled from this state, which is thus fully bound entangled. Then we show that this state nevertheless violates a Bell inequality. Our result also disproves the multipartite version of a longstanding conjecture made by Asher Peres.