Local state antimarking : Nonlocality without entanglement

TL;DR

This paper explores nonlocality without entanglement through local state antidistinguishability and antimarking, revealing new forms of quantum nonlocality in multipartite systems.

Contribution

It introduces the task of local state antimarking (LSAM), demonstrating nonlocality without entanglement in product states and comparing it with related quantum discrimination paradigms.

Findings

Any ensemble of mutually orthogonal multipartite pure states is locally antidistinguishable.

An ensemble of product states exhibits nonlocality without entanglement via LSAM.

No strict hierarchy exists among LSAD, LSAM, and local state discrimination tasks.

Abstract

A set of quantum states is said to be antidistinguishable if, upon being given a randomly chosen state, it is possible to identify a state that the system was definitively not prepared in. In this work, we begin with a study of quantum nonlocality within the framework of local state antidistinguishability (LSAD), and find that any ensemble of mutually orthogonal multipartite pure states is locally antidistinguishable. We then extend this paradigm by introducing the task of local state antimarking (LSAM), where a non-repetitive sequence from a known set of multipartite states is randomly selected and distributed to spatially separated parties who must identify at least one sequence that was not supplied using LOCC only. We present an ensemble of product states that is not globally antidistinguishable, but choosing states from it, without replacement, produces such sequences of states which are globally antidistinguishable but not locally-revealing a form of nonlocality without entanglement. Finally, we compare LSAD and LSAM with conclusive local state discrimination and conclusive local state marking. We demonstrate that no strict hierarchy exists between these paradigms: there exist product-state ensembles that permit one task while strictly forbidding the other, and vice versa.