Majorisation-minimisation algorithm for optimal state discrimination in quantum communications

Designing optimal measurement operators for quantum state discrimination (QSD) is an important problem in quantum communications and cryptography applications. Prior works have demonstrated that optimal quantum measurement operators can be obtained by solving a convex semidefinite program (SDP). However, solving the SDP can represent a high computational burden for many real-time quantum communication systems. To address this issue, a majorisation-minimisation (MM)-based algorithm, called Quantum Majorisation-Minimisation (QMM) is proposed for solving the QSD problem. In QMM, the authors reparametrise the original objective, then tightly upper-bound it at any given iterate, and obtain the next iterate as a closed-form solution to the upper-bound minimisation problem. Our numerical simulations demonstrate that the proposed QMM algorithm significantly outperforms the state-of-the-art SDP algorithm in terms of speed, while maintaining comparable performance for solving QSD problems in quantum communication applications.