One-Way Quantum Secure Direct Communication with Choice of Measurement Basis as the Secret

TL;DR

This work investigates one-way quantum secure direct communication (QSDC) where the secret bit is encoded in the local choice between the $Z$ and $X$ measurement bases. It builds a state-based framework using finite ensembles of shared EPR pairs per bit and a public authenticated channel, and analyzes security through the quantum wiretap channel formalism under BB84-symmetric attacks, with a focus on practical star-network implementations that avoid receiver unitaries. The paper extends the CDM06 protocol by removing entanglement distillation and exploring four public-channel disclosure schemes, showing that arbitrarily secure direct communication is possible at low QBERs via suitable coding, while quantifying achievable secure net bit rates and their dependence on ensemble size. Overall, the approach provides a principled route to secure one-way QSDC with measurement-basis secrecy, offering robustness to certain errors and applicability to real-world network topologies, though with rates generally lower than established QSDC protocols in zero-error scenarios. Key contributions include a detailed state-based formulation, a BB84-symmetric security analysis with numerical optimization, and practical guidance for implementing star-network QSDC without local unitaries.

Abstract

Motivated by the question of the distinguishability of ensembles described by the same compressed density operator, we propose a model for one-way quantum secure direct communication using finite ensembles of shared EPR pairs per bit and a public authenticated classical channel, where the local choice of one of two mutually-unbiased measurement bases is the secret bit. In this model, both the encoding and decoding of classical information in quantum systems are implemented by measurements in either the computational or the Hadamard basis. Using the quantum wiretap channel theory, we study the secure net bit rates and certify information-theoretic security of different implementations of our model when the quantum channel is subjected to BB84-symmetric attacks. Since no local unitary operations need to be performed by the receiver, the proposed model is suitable for real-life implementation of secure direct communication in star network configurations.

Figures (2)

• Figure 1: Secure net bit rates per ensemble (top) and per EPR pair (bottom) achievable by four different implementations of our model as functions of the size of the ensembles. These rates were computed for a one-way quantum channel with fixed qubit error rates $Q_Z=Q_X=0.05$.
• Figure 2: Colormaps representing the secure net bit rates per EPR pair achievable by four different implementations of our model as functions of the qubit error rates in the $Z$ and $X$ bases. The colormaps suggest that the model is more robust to phase-flip than to bit-flip errors, as expected from its asymmetry. For sufficiently high qubit error rates (corresponding to the completely dark regions), secure communication cannot be ensured. All rates were computed for an ensemble size of $n=2$.