@article{bibcite_16180,
  author = {Ludmi{\l}a Marcinkowska and {\L}ukasz Pawela and Marcin Markiewicz and Zbigniew Pucha{\l}a},
  title = {Asymptotic distinguishability of Haar-averaged measurement models},
  abstract = {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^(x)(n$_{1}$+n$_{2}$) with U ∈ U(d), and another induced by independent local unitaries U$_{1}$^(x)n$_{1}$ (x) U$_{2}$^(x)n$_{2}$. 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 {\textrightarrow} 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.},
  year = {2026},
  journal = {arXiv:2605.31168},
  pages = {49},
  month = {05/29/2026},
  url = {https://arxiv.org/abs/2605.31168},
  doi = {10.48550/arXiv.2605.31168},
}