Rooted-tree network for optimal non-local gate implementation

TL;DR

This paper introduces a rooted-tree quantum network structure that optimizes the implementation of non-local control-unitary gates across multiple parties with minimal entanglement, generalizing previous models.

Contribution

It proposes a novel rooted-tree network framework for efficient non-local gate implementation, extending to arbitrary multi-party scenarios and unifying previous network models.

Findings

Rooted-tree structure minimizes entanglement cost for non-local gates

Demonstrates implementation of control-Hermitian and control-unitary gates in multi-party networks

Generalizes and unifies existing quantum network models

Abstract

A general quantum network for implementing non-local control-unitary gates, between remote parties at minimal entanglement cost, is shown to be a rooted-tree structure. Starting from a five party scenario, we demonstrate the local implementation of simultaneous control-Hermitian and multiparty control-unitary gates in an arbitrary n-party network. Previously established networks are shown to be special cases of this general construct.