Quantum secure direct communication with private dense coding using general preshared quantum state

TL;DR

This paper introduces a quantum secure direct communication protocol leveraging a general preshared quantum state and dense coding, ensuring security even against eavesdroppers with access to joint systems, and provides practical bounds for finite-length scenarios.

Contribution

It develops a novel quantum communication protocol using a general preshared state and group-based unitaries, with security guarantees and practical leakage bounds.

Findings

Eve obtains no information even with joint system access.

A concrete protocol with finite-length leakage bounds is proposed.

Application to unknown preshared states using discrete Weyl-Heisenberg representation.

Abstract

We study quantum secure direct communication by using a general preshared quantum state and a generalization of dense coding. In this scenario, Alice is allowed to apply a unitary on the preshared state to encode her message, and the set of allowed unitaries forms a group. To decode the message, Bob is allowed to apply a measurement across his own system and the system he receives. In the worst scenario, we guarantee that Eve obtains no information for the message even when Eve access the joint system between the system that she intercepts and her original system of the preshared state. For a practical application, we propose a concrete protocol and derive an upper bound of information leakage in the finite-length setting. We also discuss how to apply our scenario to the case with discrete Weyl-Heisenberg representation when the preshared state is unknown.