Local implementation of nonlocal operations of block forms

TL;DR

This paper explores how to implement nonlocal block matrix operations locally across multiple parties, providing protocols that generalize bipartite methods to multiparty scenarios and comparing these with remote local operations.

Contribution

It introduces a protocol for local implementation of nonlocal block operations applicable to multiparty systems, extending bipartite techniques and analyzing their relation to remote operations.

Findings

Protocols for local implementation of nonlocal block operations

Generalization from bipartite to multiparty cases

Comparison between local and remote implementation methods

Abstract

We investigate the local implementation of nonlocal operations with the block matrix form, and propose a protocol for any diagonal or offdiagonal block operation. This method can be directly generalized to the two-party multiqubit case and the multiparty case. Especially, in the multiparty cases, any diagonal block operation can be locally implemented using the same resources as the multiparty control-U operation discussed in Ref. [Eisert et al., Phys. Rev. A 62, 052317(2000)]. Although in the bipartite case, this kind of operations can be transformed to control-U operation using local operations, these transformations are impossible in the multiparty cases. We also compare the local implementation of nonlocal block operations with the remote implementation of local operations, and point out a relation between them.