Fast protocols for local implementation of bipartite nonlocal unitaries

TL;DR

This paper introduces two fast protocols that significantly reduce communication time for implementing certain bipartite nonlocal unitaries using entanglement and LOCC, with efficiency improvements demonstrated through examples.

Contribution

The paper presents novel fast protocols for bipartite nonlocal unitaries that cut communication time in half, expanding the toolkit for efficient quantum operations.

Findings

Communication time reduced by a factor of two

Protocols are efficient for some simple unitaries

Set of implementable unitaries may expand with more entanglement

Abstract

In certain cases the communication time required to deterministically implement a nonlocal bipartite unitary using prior entanglement and LOCC (local operations and classical communication) can be reduced by a factor of two. We introduce two such "fast" protocols and illustrate them with various examples. For some simple unitaries, the entanglement resource is used quite efficiently. The problem of exactly which unitaries can be implemented by these two protocols remains unsolved, though there is some evidence that the set of implementable unitaries may expand at the cost of using more entanglement.