Prior entanglement between senders enables perfect quantum network coding with modification

TL;DR

This paper presents a protocol that uses prior entanglement between senders to enable perfect quantum network coding in a butterfly network, achieving efficient transmission with minimal communication and proving impossibility without entanglement.

Contribution

It introduces a novel protocol leveraging prior entanglement for perfect quantum network coding and establishes the fundamental necessity of entanglement for this task.

Findings

Protocol achieves perfect transmission with minimal qubit or classical bits.

Impossible to achieve the same without prior entanglement, as shown by fidelity bounds.

Provides theoretical proof of the essential role of entanglement in quantum network coding.

Abstract

We find a protocol transmitting two quantum states crossly in the butterfly network only with prior entanglement between two senders. This protocol requires only one qubit transmission or two classical bits transmission in each channel in the butterfly network. It is also proved that it is impossible without prior entanglement. More precisely, an upper bound of average fidelity is given in the butterfly network when prior entanglement is not allowed.