Asymptotic distinguishability of Haar-averaged measurement models
| Autorzy | Marcinkowska L.; Pawela Ł.; Markiewicz M.; Puchała Z. |
|---|---|
| Tytuł | Asymptotic distinguishability of Haar-averaged measurement models |
| Czasopismo | arXiv:2605.31168 |
| Rok | 2026 |
| Status | Submitted |
| Strony | 49 |
| DOI | 10.48550/arXiv.2605.31168 |
| URL | https://arxiv.org/abs/2605.31168 |
| Abstrakt | 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. |
| 2605.31168v1.pdf |