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.
Bound-entangled states with positive partial transpose (PPT) can exhibit quantum steering and Bell nonlocality, disproving the long-standing Peres conjecture and its stronger steering counterpart. These counterexamples, obtained through explicit constructions or numerical searches, raise the question of whether they share a common structural origin. We address this question in the low-rank regime by asking whether known counterexamples can be obtained, up to invertible local filtering, from the complement of an unextendible product basis (UPB). We find that the answer depends crucially on the local dimension. In
3⊗3, the rank-four structure of PPT entangled states implies that both the steerable PPT state of Moroder \textit{et al.} and the Bell-nonlocal PPT state of Vértesi and Brunner can be obtained from UPB-complement states under invertible local filtering. For three qubits, in contrast, rank-four states that are PPT across every bipartition are separable across each cut. Moreover, comparison of the product-vector structure of the relevant kernels shows that the known three-qubit Bell-nonlocal PPT states cannot be obtained by invertible local filtering from the complement of any three-qubit UPB. Going beyond rank four, we further show that a known rank-eight three-qutrit state, supported on the complement of a UPB and PPT across every bipartition, is genuinely multipartite entangled. These results show that UPBs provide a unifying structural origin for important low-rank PPT entangled states in
3⊗3, but that nonlocal bound entanglement is not, in general, a UPB phenomenon.
Bound entanglement, being entangled yet not distillable, is essential to our understanding 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 construct this kind of nonlocal bound entangled state for all finite dimensions larger than two, making possible their experimental demonstration in 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.
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 long-standing conjecture made by Peres.