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<xml><records><record><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Ludmiła Marcinkowska</style></author><author><style face="normal" font="default" size="100%">Łukasz Pawela</style></author><author><style face="normal" font="default" size="100%">Marcin Markiewicz</style></author><author><style face="normal" font="default" size="100%">Zbigniew Puchała</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Asymptotic distinguishability of Haar-averaged measurement models</style></title></titles><keywords/><dates><year><style face="normal" font="default" size="100%">2026</style></year><pub-dates><date><style face="normal" font="default" size="100%">05/29/2026</style></date></pub-dates></dates><secondary-title><style face="normal" font="default" size="100%">arXiv:2605.31168</style></secondary-title><urls><style face="normal" font="default" size="100%">https://arxiv.org/abs/2605.31168</style></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.48550/arXiv.2605.31168</style></electronic-resource-num><pages><style face="normal" font="default" size="100%">49</style></pages><abstract><style face="normal" font="default" size="100%">We study discrimination problems generated by the same basic Haar-random measurement mechanism at two observational levels. First, we derive an explicit expression for the type-II error in the task of discriminating a Haar-random measure-and-prepare channel from the identity channel I, using a coherence-sensitive entangled tester. Second, after passing to the induced classical measurement records, we compare two random measurement models: one induced by a single collective unitary of the form U^⊗(n₁+n₂) with U ∈ U(d), and another induced by independent local unitaries U₁^⊗n₁ ⊗ U₂^⊗n₂. For the associated Haar-averaged aggregate histogram laws, in which the block of origin of each count is not retained, we obtain closed-form formulas and quantify their discrepancy through the total variation distance. We derive asymptotic expressions in the fixed-N, large-d regime, the fixed-d, large-N regime, the sparse joint-scaling regime N = o(√d), and the critical scaling regime N/√d → c. We also identify the block-resolved pair-of-histograms law, showing that the aggregate total variation distance is a coarse-grained lower bound on the distinguishability available when block labels are retained.</style></abstract></record></records></xml>
