We show that the second law of thermodynamics poses a restriction on how well we can discriminate between quantum states. By examining an ideal gas with a quantum internal degree of freedom undergoing a cycle based on a proposal by Peres, we establish a nontrivial upper bound on the attainable accuracy of quantum state discrimination. This thermodynamic bound, which relies solely on the linearity of quantum mechanics and the constraint of no work extraction, matches Holevo's bound on accessible information, but is looser than the Holevo-Helstrom bound. The result gives more evidence on the disagreement between thermodynamic entropy and von Neumann entropy and places potential limitations on proposals beyond quantum mechanics.

• Received 12 June 2023
• Accepted 7 November 2023

DOI:https://doi.org/10.1103/PhysRevE.109.014119