Conclusive Local State Marking: More Nonlocality With No Entanglement

TL;DR

This paper introduces conclusive local state marking, a new quantum discrimination task that uncovers a hierarchy of nonlocality, showing some product states exhibit stronger nonlocality than entangled states.

Contribution

It unifies local state discrimination and marking into a new framework, revealing a finer hierarchy of nonlocality and demonstrating stronger nonlocality in certain product state ensembles.

Findings

Certain product state ensembles exhibit stronger nonlocality than entangled ensembles.

The new task reveals a hierarchy of nonlocality in multipartite quantum states.

Unification of local state discrimination and marking into a conclusive framework.

Abstract

Nonlocality exhibited by ensembles of composite quantum states, wherein local operations and classical communication (LOCC) yield suboptimal discrimination probabilities compared to global strategies, is one of the striking nonclassical features of quantum theory. A variant of this phenomenon arises in conclusive local state discrimination, where the correct state must be identified with zero error, albeit allowing for inconclusive outcomes. More recently, the notion of local state marking has been introduced, with the focus shifted to correctly identifying the permutation of a subset of states randomly chosen from a given set of multipartite states under LOCC. In this work, we unify these two approaches by introducing the task of conclusive local state marking, which reveals a finer hierarchy of nonlocality in multipartite quantum state ensembles. Notably, we demonstrate that certain ensembles of product states can exhibit a stronger form of nonlocality than entangled ensembles traditionally considered highly nonlocal.