Unifying quantum measurement constructions via a relative-entropy minimum change principle

• URL: http://arxiv.org/abs/2608.04055v1
• Date: Tue, 04 Aug 2026 11:14:40 GMT
• Title: Unifying quantum measurement constructions via a relative-entropy minimum change principle
• Abstract summary: The minimum change principle provides an information-theoretic characterization of the Bayes reversal channel in classical probability theory.<n>We consider a forward process based on a classical-to-quantum preparation channel and a reverse process based on a quantum-to-classical measurement channel.<n>We show that softmin thermal measurements arise as optimal solutions to entropy-regularized semidefinite optimization problems.
• Score: 12.046119801151619
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The minimum change principle provides an information-theoretic characterization of the Bayes reversal channel in classical probability theory and has recently been proposed as a framework for extending Bayes' rule to quantum information theory. Using quantum relative entropy, we investigate a minimum change principle for the setting of quantum statistical inference. Specifically, we consider a forward process based on a classical-to-quantum preparation channel and a reverse process based on a quantum-to-classical measurement channel. We establish a closed-form characterization of measurements that are optimal for this principle, and this optimal measurement can be found via a dual formulation involving a single unconstrained Hermitian variable. This perspective allows us to recover some notable measurements within the same framework, including pretty good measurements and Fermi-Dirac thermal measurements, and we use it to discover a novel family that we call softmin thermal measurements. We further show that softmin thermal measurements arise as optimal solutions to entropy-regularized semidefinite optimization problems, demonstrating that they play a role for measurements analogous to that of thermal states in statistical mechanics. Finally, we prove an additivity property for the relative-entropy minimum change principle and investigate the performance of Fermi-Dirac thermal measurements for quantum hypothesis testing.

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