Quantum Network Code for Multiple-Unicast Network with Quantum Invertible Linear Operations

TL;DR

This paper introduces a quantum network coding scheme for multiple-unicast networks with invertible linear node operations, enabling secure, interference-free quantum communication for multiple sender-receiver pairs without classical communication.

Contribution

It generalizes previous quantum unicast codes to multiple-unicast networks, providing a construction that guarantees secure quantum transmission under linear node operation restrictions.

Findings

Achieves asymptotic quantum state transmission for each user

Ensures no information leakage between users

Operates solely with sender and receiver coding, no classical communication

Abstract

This paper considers the communication over a quantum multiple-unicast network where r sender-receiver pairs communicate independent quantum states. We concretely construct a quantum network code for the quantum multiple-unicast network as a generalization of the code [Song and Hayashi, arxiv:1801.03306, 2018] for the quantum unicast network. When the given node operations are restricted to invertible linear operations between bit basis states and the rates of transmissions and interferences are restricted, our code certainly transmits a quantum state for each sender-receiver pair by n-use of the network asymptotically, which guarantees no information leakage to the other users. Our code is implemented only by the coding operation in the senders and receivers and employs no classical communication and no manipulation of the node operations. Several networks that our code can be applied are also given.