Perfect Quantum Network Communication Protocol Based on Classical Network Coding

TL;DR

This paper demonstrates that perfect quantum communication over a network without prior entanglement can be achieved at rates bounded by classical network coding principles, linking quantum capacity with classical min-cut max-flow theorems.

Contribution

It establishes a fundamental connection between quantum communication capacity and classical network coding bounds, providing a new theoretical framework for quantum network protocols.

Findings

Quantum capacity bounds are given by classical min-cut max-flow theorem.

No prior entanglement is required for the quantum communication protocol.

The protocol achieves perfect quantum state transfer under the given conditions.

Abstract

This paper considers a problem of quantum communication between parties that are connected through a network of quantum channels. The model in this paper assumes that there is no prior entanglement shared among any of the parties, but that classical communication is free. The task is to perfectly transfer an unknown quantum state from a source subsystem to a target subsystem, where both source and target are formed by ordered sets of some of the nodes. It is proved that a lower bound of the rate at which this quantum communication task is possible is given by the classical min-cut max-flow theorem of network coding, where the capacities in question are the quantum capacities of the edges of the network.