A Game-Theoretic Approach with Decoy Qubits for Quantum Superdense Coding Security

Quantum superdense coding protocol is addressed in the literature as a promising approach for efficient quantum communication. It allows two parties, to transmit classical bits using quantum bits. However, its security is threatened by a scrambling attack that involves modifying the automated gate specification to effectively scramble the final measurement, and by a bijection attack that performs a bijective transformation on the final measured strings. In this paper, we propose a novel approach to preventing such attacks by introducing decoy qubits into the superdense coding protocol, which act as a source of randomness that can detect any tampering with the entangled states and enable the detection of an eavesdropper. To strategize the selection and sending of these decoy qubits and address the interaction between the sender, receiver, and eavesdropper, we propose a dynamic non-cooperative game-based approach evaluated with a Q-learning algorithm to model and analyze this problem as a benefit-cost model. The utility functions of the proposed game are based on the concepts of return on protection, which illustrates the gain of selecting and sending a decoy qubit, and return on attack, which illustrates the reward of the eavesdropper for performing an attack to compromise the communication. Moreover, we discuss and analyze the Nash equilibrium convergence of this attack-defense model. Finally, we perform simulation work using a Q-learning algorithm to show the effectiveness of the proposed model in assessing the behavior of the players and its ability to reach equilibrium within a finite number of steps.