01652nas a2200157   4500000000100000008004100001260001500042100002600057700001900083700002200102700002200124245007000146856003700216300000700253520123400260       2026                            d  c05/29/20261 aLudmiła Marcinkowska1 aŁukasz Pawela1 aMarcin Markiewicz1 aZbigniew Puchała00aAsymptotic distinguishability of Haar-averaged measurement models  uhttps://arxiv.org/abs/2605.31168  a493 aWe 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.