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<xml><records><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_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/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2026</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">arXiv:2605.31168</style></SECONDARY_TITLE><PAGES><style face="normal" font="default" size="100%">49</style></PAGES><DATE><style face="normal" font="default" size="100%">05/29/2026</style></DATE><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><URL><style face="normal" font="default" size="100%">https://arxiv.org/abs/2605.31168</style></URL><title><style face="normal" font="default" size="100%">Asymptotic distinguishability of Haar-averaged measurement models</style></title></RECORD></records></xml>
