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Research questionWhat statistical guarantees can quantum maximum-likelihood prediction provide from finite iid samples?Quantum maximum-likelihood prediction represents empirical probability distributions as quantum states and fits them by minimizing quantum relative entropy over a chosen class of states. The central difficulty is characterizing finite-sample convergence and concentration, as well as when information projections exist in finite- or infinite-dimensional settings.
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Latest papersRecent research connected to this question, newest first.Quantum Maximum Likelihood Prediction via Hilbert Space EmbeddingsThe source studies a quantum analogue of maximum-likelihood prediction for iid samples. It provides non-asymptotic guarantees in trace norm and quantum relative entropy, and analyzes quantum information projection, including a Pythagorean inequality for mixture families under possibly non-self-adjoint linear constraints and in infinite dimensions when a finite minimum is attained.research paper · Sep 2, 2026
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