Local Distinguishability of Multipartite Unitary Operations

TL;DR

This paper proves that any two different multipartite unitary operations can be perfectly distinguished using only local operations and classical communication, even when multiple operations are involved, without requiring entanglement.

Contribution

It demonstrates that nonlocal unitary operations' identities can be recovered locally, extending the distinguishability to multiple operations without entanglement.

Findings

Any two different unitary operations are locally distinguishable with finite runs.

The result extends to multiple unitary operations beyond two.

Local distinguishability does not require entanglement or joint operations.

Abstract

We show that any two different unitary operations acting on an arbitrary multipartite quantum system can be perfectly distinguishable by local operations and classical communication when a finite number of runs is allowed. We then directly extend this result into the case when the number of unitary operations to be discriminated is more than two. Intuitively, our result means that the lost identity of a nonlocal (entangled) unitary operation can be recovered locally, without any use of entanglement or joint quantum operations.