The Basics of Perfect Communication through Quantum Networks

TL;DR

This paper characterizes the conditions for perfect quantum state transfer in networks, exploring limitations and trade-offs imposed by network topology, interaction types, and transfer rate constraints.

Contribution

It provides necessary and sufficient conditions for quantum state transfer in constrained networks and analyzes the resulting limitations and trade-offs.

Findings

Certain network topologies cannot support routing for many recipients.

Transfer rate limitations are inherent in specific Hamiltonian models.

Trade-offs exist between transfer distance and network size in uniform coupling models.

Abstract

Perfect transfer of a quantum state through a one-dimensional chain is now well understood, allowing one not only to decide whether a fixed Hamiltonian achieves perfect transfer, but to design a suitable one. We are particularly interested in being able to design, or understand the limitations imposed upon, Hamiltonians subject to various naturally arising constraints such as a limited coupling topology with low connectivity (specified by a graph) and type of interaction. In this paper, we characterise the necessary and sufficient conditions for transfer through a network, and describe some natural consequences such as the impossibility of routing between many different recipients for a large class of Hamiltonians, and the limitations on transfer rate. We also consider some of the trade-offs that arise in uniformly coupled networks (both Heisenberg and XX models) between transfer distance and the size of the network as a consequence of the derived conditions.