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Free, publicly-accessible full text available December 16, 2025
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Abstract We study the capacity of entanglement as an alternative to entanglement entropies in estimating the degree of entanglement of quantum bipartite systems over fermionic Gaussian states. In particular, we derive the exact and asymptotic formulas of average capacity of two different cases—with and without particle number constraints. For the later case, the obtained formulas generalize some partial results of average capacity in the literature. The key ingredient in deriving the results is a set of new tools for simplifying finite summations developed very recently in the study of entanglement entropy of fermionic Gaussian states.more » « less
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We show here thatmir-279/996are absolutely essential for development and function of Johnston's organ (JO), the primary proprioceptive and auditory organ inDrosophila. Their deletion results in highly aberrant cell fate determination, including loss of scolopale cells and ectopic neurons, and mutants are electrophysiologically deaf. In vivo activity sensors and mosaic analyses indicate that these seed-related miRNAs function autonomously to suppress neural fate in nonneuronal cells. Finally, genetic interactions pinpoint two neural targets (elavandinsensible) that underlie miRNA mutant JO phenotypes. This work uncovers how critical post-transcriptional regulation of specific miRNA targets governs cell specification and function of the auditory system.more » « less
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The density matrix formalism is a fundamental tool in studying various problems in quantum information processing. In the space of density matrices, the most well-known measures are the Hilbert–Schmidt and Bures–Hall ensembles. In this work, the averages of quantum purity and von Neumann entropy for an ensemble that interpolates between these two major ensembles are explicitly calculated for finite-dimensional systems. The proposed interpolating ensemble is a specialization of the [Formula: see text]-deformed Cauchy–Laguerre two-matrix model and new results for this latter ensemble are given in full generality, including the recurrence relations satisfied by their associated bi-orthogonal polynomials when [Formula: see text] assumes positive integer values.more » « less
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Abstract As an alternative to entanglement entropies, the capacity of entanglement becomes a promising candidate to probe and estimate the degree of entanglement of quantum bipartite systems. In this work, we study the statistical behavior of entanglement capacity over major models of random states. In particular, the exact and asymptotic formulas of average capacity have been derived under the Hilbert–Schmidt and Bures-Hall ensembles. The obtained formulas generalize some partial results of average capacity computed recently in the literature. As a key ingredient in deriving the results, we make use of techniques in random matrix theory and our previous results pertaining to the underlying orthogonal polynomials and special functions. Simulations have been performed to numerically verify the derived formulas.more » « less
