Induced random mixed states are symmetric Dirichlet mixtures

• URL: http://arxiv.org/abs/2609.09421v1
• Date: Tue, 08 Sep 2026 20:21:16 GMT
• Title: Induced random mixed states are symmetric Dirichlet mixtures
• Abstract summary: We recast a class of expectation values for induced ensembles into calculations involving Dirichlet moments and low-order Haar averages on a single-system state space.<n>As applications, we recover exact purity moments up to fourth order, derive the mean Hilbert--Schmidt distance between independent induced ensembles with possibly different environment dimensions, and obtain exact average determinants.
• Score: 39.60347374522111
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We establish an exact equivalence in distribution between $D$-dimensional random mixed states induced by partial traces over $K$-dimensional environments and the Mai-Alquier distribution, a mixture of $K$ independent Haar-random pure states weighted by a symmetric Dirichlet distribution. This identification recasts a class of expectation values for induced ensembles into calculations involving Dirichlet moments and low-order Haar averages on a single-system state space. As applications, we recover exact purity moments up to fourth order, derive the mean Hilbert--Schmidt distance between independent induced ensembles with possibly different environment dimensions, and obtain exact average determinants. These results provide a unified and constructive perspective on induced random mixed states and on the evaluation of quantities such as purity moments, overlaps, and determinants.

Related papers

• Characterizing Heterogeneous Rates in Finite Mixture Estimation via Partial Optimal Transport [88.55403215843967]
  Voronoi-based partial optimal transport (VPOT) for obtaining refined local and global convergence guarantees for the maximum likelihood estimator of the mixing measure.<n>Results hold in arbitrary fixed dimension without requiring mixing proportions to be uniformly bounded away from zero or prior knowledge of the true number of mixture components.
  arXiv  Detail & Related papers  (2026-09-15T04:32:53Z)
• Distributionally Faithful Imputation via Positive Semi-Definite Kernel Density Estimation [55.47411235954028]
  We recast imputation under missing completely at random as density estimation from masked observations.<n>We obtain a convex empirical risk problem with closed form marginals, solvable by a Newton interior point method.<n>The resulting PSD Impute model yields both single and multiple imputations from the same fitted density.
  arXiv  Detail & Related papers  (2026-07-08T15:51:05Z)
• Summarizing Bayesian Nonparametric Mixture Posterior -- Sliced Optimal Transport Metrics for Gaussian Mixtures [10.694077392690447]
  Existing methods to summarize posterior inference for mixture models focus on identifying a point estimate of the implied random partition for clustering.<n>We propose a novel approach for summarizing posterior inference in nonparametric Bayesian mixture models, prioritizing estimation of the mixing measure (or mixture) as an inference target.
  arXiv  Detail & Related papers  (2024-11-22T02:15:38Z)
• Mixing of the No-U-Turn Sampler and the Geometry of Gaussian Concentration [0.0]
  We prove that the mixing time of the No-U-Turn Sampler (NUTS) scales as $d1/4$, up to logarithmic factors, where $d$ is the dimension. Specifically, concentration of measure results in a striking uniformity in NUTS' locally adapted transitions, which holds with high probability.
  arXiv  Detail & Related papers  (2024-10-09T15:17:01Z)
• Consistency for constrained maximum likelihood estimation and clustering based on mixtures of elliptically-symmetric distributions under general data generating processes [0.0]
  In a situation where $P$ is a mixture of well enough separated but nonparametric distributions it is shown that the components of the population version of the estimator correspond to the well separated components of $P$. This provides some theoretical justification for the use of such estimators for cluster analysis in case that $P$ has well separated subpopulations even if these subpopulations differ from what the mixture model assumes.
  arXiv  Detail & Related papers  (2023-11-10T15:20:39Z)
• Adaptive Annealed Importance Sampling with Constant Rate Progress [68.8204255655161]
  Annealed Importance Sampling (AIS) synthesizes weighted samples from an intractable distribution. We propose the Constant Rate AIS algorithm and its efficient implementation for $alpha$-divergences.
  arXiv  Detail & Related papers  (2023-06-27T08:15:28Z)
• Targeted Separation and Convergence with Kernel Discrepancies [61.973643031360254]
  kernel-based discrepancy measures are required to (i) separate a target P from other probability measures or (ii) control weak convergence to P.<n>In this article we derive new sufficient and necessary conditions to ensure (i) and (ii)<n>For MMDs on separable metric spaces, we characterize those kernels that separate Bochner embeddable measures and introduce simple conditions for separating all measures with unbounded kernels.
  arXiv  Detail & Related papers  (2022-09-26T16:41:16Z)
• Tangent Space and Dimension Estimation with the Wasserstein Distance [10.118241139691952]
  Consider a set of points sampled independently near a smooth compact submanifold of Euclidean space. We provide mathematically rigorous bounds on the number of sample points required to estimate both the dimension and the tangent spaces of that manifold.
  arXiv  Detail & Related papers  (2021-10-12T21:02:06Z)
• Improving application performance with biased distributions of quantum states [0.0]
  We analyze mixtures of Haar-random pure states with Dirichlet-distributed coefficients. We analytically derive the concentration parameters required to match the mean purity of the Bures and Hilbert--Schmidt distributions. We demonstrate how substituting these Dirichlet-weighted Haar mixtures in place of the Bures and Hilbert--Schmidt distributions results in measurable performance advantages.
  arXiv  Detail & Related papers  (2021-07-15T23:29:10Z)
• Consistent Estimation of Identifiable Nonparametric Mixture Models from Grouped Observations [84.81435917024983]
  This work proposes an algorithm that consistently estimates any identifiable mixture model from grouped observations. A practical implementation is provided for paired observations, and the approach is shown to outperform existing methods.
  arXiv  Detail & Related papers  (2020-06-12T20:44:22Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.