Quantum nonlocality without entanglement

TLDR

The authors show that an orthogonal set of product states of two qutrits cannot be perfectly distinguished by separated observers using any sequence of local operations and classical communication. They classify multipartite product states by their entropy and entanglement costs for preparation and measurement via local operations. They prove a finite gap between joint and local mutual information, implying that separable superoperators cannot be implemented locally, and identify additional nonlocally measurable product states.

Abstract

We exhibit an orthogonal set of product states of two three-state particles that nevertheless cannot be reliably distinguished by a pair of separated observers ignorant of which of the states has been presented to them, even if the observers are allowed any sequence of local operations and classical communication between the separate observers. It is proved that there is a finite gap between the mutual information obtainable by a joint measurement on these states and a measurement in which only local actions are permitted. This result implies the existence of separable superoperators that cannot be implemented locally. A set of states are found involving three two-state particles that also appear to be nonmeasurable locally. These and other multipartite states are classified according to the entropy and entanglement costs of preparing and measuring them by local operations.