Local Entanglement Is Not Necessary for Perfect Discrimination between Unitary Operations Acting on Two-Qudits by LOCC

TL;DR

This paper demonstrates that perfect discrimination between two-unitary operations on two-qudits can be achieved by LOCC without the need for local entanglement, challenging previous assumptions about entanglement's necessity.

Contribution

It proves that local entanglement is not required for perfect discrimination of two-qudit unitaries by LOCC, providing a new understanding of quantum operation discrimination.

Findings

Perfect discrimination achievable without local entanglement.

Local entanglement is not necessary for two-qudit unitary discrimination.

Challenges previous belief that entanglement is essential.

Abstract

Recently, the problem of discriminating multipartite unitary operations by local operations and classical communication (LOCC) has attracted significant attention. The latest work in the literature on this problem showed that two multipartite unitary operations can always be perfectly distinguished by LOCC when a finite number of runs are allowable. However, in these schemes, local entanglement (an entangled state holden by one party) was required, which seems to imply that local entanglement is necessary for perfect discrimination between unitary operations by LOCC. In this article, we show that a perfect discrimination between two unitary operations acting on a two-qudits can always be achieved without exploiting any entanglement. As a result, we conclude that local entanglement is not necessary for perfect discrimination between unitary operations acting on two-qudits by LOCC.