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

arXiv: https://arxiv.org/abs/2608.04055 · HTML: https://mlsanity.com/paper/2608.04055/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 87 references that are in the map.
- First posted on arXiv 4 Aug 2026.

## Builds on (most cited first, 11 of 11)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Quantum SDP-Solvers: Better upper and lower bounds](https://mlsanity.com/paper/1705.01843/) (2017)
- [Quantum-Assisted Learning of Hardware-Embedded Probabilistic Graphical Models](https://mlsanity.com/paper/1609.02542/) (2016)
- [Quantum thermodynamics and semi-definite optimization](https://mlsanity.com/paper/2505.04514/) (2025)
- [Fermi-Dirac thermal measurements: A framework for quantum hypothesis testing and semidefinite optimization](https://mlsanity.com/paper/2603.04061/) (2026)
- [Fast randomized entropically regularized semidefinite programming](https://mlsanity.com/paper/2303.12133/) (2023)
- [Quantum Fisher information matrices from R'enyi relative entropies](https://mlsanity.com/paper/2510.02218/) (2025)
- [Performance Guarantees for Quantum Neural Estimation of Entropies](https://mlsanity.com/paper/2511.19289/) (2025)
- [Fermi-Dirac machines as quantizations of neurons](https://mlsanity.com/paper/2605.24386/) (2026)
- [Optimal self-concordant barriers for quantum relative entropies](https://mlsanity.com/paper/2205.04581/) (2022)
- [Interior Point Methods for Structured Quantum Relative Entropy Optimization Problems](https://mlsanity.com/paper/2407.00241/) (2024)

## Abstract (arXiv)

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.