Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.29696

Quantum f-divergences from retrodiction: a unifying classical variational principle

Francesco Buscemi
View original source ↗Read source document ↗Export metadata ↓

Abstract

The same classical f-divergence admits inequivalent extensions to quantum states. The question is whether these extensions can be obtained from a common operational variational principle. Here we generalize Matsumoto's reverse-test optimization by introducing a reference prior state. More explicitly, we minimize the statistical distinguishability between a forward and a reverse prepare-and-measure process, related by retrodiction through the chosen reference and subject to prescribed quantum averages. Distinguishability is quantified by the classical f-divergence between their complete records. For faithful states in finite dimension, we prove that the same spectral implementation attains the minimum simultaneously for every operator-convex f. Varying the reference allows us to interpolate between standard and maximal quantum f-divergences of the prescribed states, passing through the geodesic family. More precisely, a flat reference yields the standard quantum f-divergences, thereby giving the Nussbaum-Szkoła distributions a variational characterization as optimal records. Choosing either prescribed state as reference recovers maximal quantum f-divergences and Matsumoto's reverse tests, while power references realize the geodesic interpolation. In the relative-entropy case, this gives the passage from Umegaki to Belavkin-Staszewski relative entropy by changing the prior for retrodiction.

Explore related subjects

quant-phcs.ITmath-phmath.ITmath.MP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Francesco Buscemi. 2026-10-21. Quantum f-divergences from retrodiction: a unifying classical variational principle. https://arxiv.org/abs/2610.29696

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Macroscopic quantum coherence and entanglement in mechanical systems

The notion of a macroscopic quantum state must be pinned down in order to assess how well experiments probe the large-scale limits of quantum mechanics. However, the issue of quantifying so-called quantum macroscopicity is fraught with multiple approaches having varying interpretations and levels of computability and measurability. Here, we introduce two measures that capture independent macroscopic properties: i) extensive size, measuring the degree of coherence in position or momentum observables relative to atomic-scale units, and ii) entangled size, quantifying the number of entangled subsystems. These measures unify many desirable features of past proposals while having rigorously justified interpretations from quantum information theory in terms of coherence and multipartite entanglement. We demonstrate how to estimate them and obtain lower-bounds using experimental data from micro-mechanical oscillators and diffracting molecules. Notably, we find evidence for genuine multipartite entanglement of $10^5$ to $10^7$ atoms in recent mechanical superposition states.

quant-ph↗
arXiv2026

The Quantum Channels of the Compton Scattering of an Entangled Pair of Photons

The Compton scattering of an entangled pair of photons is studied. Using the resulting reduced density matrix, we demonstrate how to derive the Kraus operators for the interaction from the underlying fundamental theory, quantum electrodynamics. The normalization of the final density matrix of the entangled photons after the interaction is crucial to obtaining the correct probabilities and correlations. The reduced density matrix of the photon, which does not participate in the interaction directly, remains unchanged. It indicates that quantum effects in quantum sensing using an entangled photon pair can be observed only through the correlations or superposition of the entire pair. We relate our results to the Stokes parameters for determining polarizations and investigating the entangled states of photons from electron-positron annihilation in astrophysical systems.

quant-ph↗
arXiv2026

Quantum-Inspired Optimization Process for Data Imputation

Data imputation is a critical preprocessing step, particularly in clinical datasets where missingness can bias downstream inference. We propose a quantum-inspired imputation framework and evaluate it on the UCI Pima Indians Diabetes dataset, where several physiological variables contain structural zeros that are treated as missing. The approach combines Principal Component Analysis (PCA) with quantum rotation-based reconstruction, where rotation angles are selected via gradient-free optimizers (Simulated Annealing, COBYLA, and Differential Evolution). For robustness, we retain the top three optimizer solutions per method and reconstruct missing values under distribution-aware bounds (e.g., $\pm 2$ standard deviations) and avoid unrealistic collapse toward central tendency. We also benchmark against (i) classical baselines (Mean, KNN, MICE, Decision Tree), (ii) modern matrix/ML imputers (SoftImpute, MissForest, VAE), and (iii) rotation/PCA controls (random orthogonal rotations and bootstrap PCA). Across the evaluated features, quantum-inspired variants achieve substantially improved distributional fidelity under Wasserstein W1 relative to modern baselines (e.g., the best quantum setting reduces average W1 by $\sim$66% vs. SoftImpute, $\sim$84% vs. MissForest, and $\sim$90% vs. VAE; and by $\sim$60% vs. Mean imputation), while remaining competitive with strong classical/control configurations. Dispersion is better preserved under the quantum-inspired methods, with variance/SD ratios closer to the observed data than (SoftImpute, MissForest, and VAE) and typically better than (Mean, KNN, MICE, and Decision Tree) on average. Overall, the results support quantum-inspired, optimization-guided rotations as a statistically grounded and scalable strategy for realistic imputation in healthcare and general AI pipelines, with a design that can be mapped to future quantum hardware as it matures.

quant-ph↗