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

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 implementations of secure direct communication in star network configurations.