Local Marking of Locally Implementable Unitary Operations

TL;DR

This paper explores local marking of multipartite quantum unitaries, revealing that local markability does not imply distinguishability and demonstrating nonlocality without entanglement.

Contribution

It introduces the concept that local marking is distinct from discrimination, constructs examples of nonlocality without entanglement, and analyzes the hierarchy of probes in local marking.

Findings

Locally markable unitaries are not necessarily distinguishable.

Constructed tripartite product unitaries that are globally distinguishable but not locally markable.

Marking a subset of unitaries does not extend to larger subsets.

Abstract

We investigate the task of local marking for locally implementable unitary operations. In this setting, multipartite quantum unitary channels, chosen randomly from a known set, are distributed among spatially separated parties without revealing their identities. The objective is to correctly identify (mark) the applied process using only local operations supplemented with classical communication (LOCC). While local distinguishability implies local marking, local marking does not guarantee either local or even global distinguishability of a set of unitaries. Thus the task of marking is not equivalent to the task of discrimination. We demonstrate a stronger manifestation of nonlocality without entanglement by constructing a set of globally distinguishable tripartite product unitaries that cannot be locally marked. In contrast to state marking, we find that marking a subset of product unitaries does not imply the ability to mark a larger subset. Finally, we explore the hierarchy of probes-entangled and product-in the context of local marking with respect to the standard discrimination scenario.