Asymptotic distinguishability of Haar-averaged measurement models
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917547779031040 |
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| author | Marcinkowska, Ludmiła Pawela, Łukasz Markiewicz, Marcin Puchała, Zbigniew |
| author_facet | Marcinkowska, Ludmiła Pawela, Łukasz Markiewicz, Marcin Puchała, Zbigniew |
| contents | 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 $\mathbb{I}$, 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 $U^{\otimes (n_1+n_2)}$ with $U\in U(d)$, and another induced by independent local unitaries $U_1^{\otimes n_1}\otimes U_2^{\otimes n_2}$. 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 $N=o(\sqrt d)$, and the critical scaling regime $N/\sqrt d\to c$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_31168 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotic distinguishability of Haar-averaged measurement models Marcinkowska, Ludmiła Pawela, Łukasz Markiewicz, Marcin Puchała, Zbigniew Quantum Physics 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 $\mathbb{I}$, 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 $U^{\otimes (n_1+n_2)}$ with $U\in U(d)$, and another induced by independent local unitaries $U_1^{\otimes n_1}\otimes U_2^{\otimes n_2}$. 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 $N=o(\sqrt d)$, and the critical scaling regime $N/\sqrt d\to c$. 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. |
| title | Asymptotic distinguishability of Haar-averaged measurement models |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.31168 |