Carnot Meets Quantum Information: Thermal Machine Driven by Probabilistic Non-orthogonal State Discrimination

Abstract

While the impossibility of perfectly identifying non-orthogonal states is a cornerstone of quantum information science, their probabilistic discrimination is nonetheless permissible. Here, we propose a two-reservoir quantum machine driven by this mechanism to map its functional boundaries across the parameter space of the state overlap $μ$ and the Carnot efficiency $η_C$. Within this $η_C$-$μ$ plane, the machine exhibits phase-transition-like functional switching among a pure heat-engine phase, a mixed phase, and a dissipative phase. We identify critical thresholds governing these transitions: strong thermal driving ($η_C \ge 0.5$) unconditionally guarantees positive work extraction, whereas weak driving ($η_C \lesssim 0.13$) induces an anomalous reentrant transition, where increasing $μ$ unexpectedly restores engine functionality after a purely dissipative regime. Our results explicitly demonstrate how quantum mechanics and thermodynamics jointly constrain information-to-energy conversion.