Balancing the minimum error rate and minimum copy consumption in quantum state discrimination

Extracting more information and saving quantum resources are two main aims for quantum measurements. However, the optimization of strategies for these two objectives varies when discriminating between quantum states <inline-formula><tex-math id="M2222">\begin{document}$ |\psi_0\rangle$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0155_M2222.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0155_M2222.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M99">\begin{document}$|\psi_1\rangle $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0155_M99.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0155_M99.png"/></alternatives></inline-formula> through multiple measurements. In this study, we introduce a novel state discrimination model that reveals the intricate relationship between the average error rate and average copy consumption. By integrating these two crucial metrics and minimizing their weighted sum for any given weight value, our research underscores the infeasibility of simultaneously minimizing these metrics through local measurements with one-way communication. Our findings present a compelling trade-off curve, highlighting the advantages of achieving a balance between error rate and copy consumption in quantum discrimination tasks, offering valuable insights into the optimization of quantum resources while ensuring the accuracy of quantum state discrimination.