bibkey: bohac2025biasclassqram
authors: Leonardo Bohac
year: 2025
title: "Bias-Class Discrimination of Universal QRAM Boolean Memories"
doi: 10.48550/arXiv.2512.17503
url: "https://arxiv.org/abs/2512.17503v1"
claim: "The paper derives the single-query ensemble state and the single-copy Helstrom test for exact-weight bias classes of Boolean memories queried through a universal QRAM, gives a separable multi-query strategy based on the count of plus outcomes, and leaves open whether that count statistic is sufficient for optimal discrimination."
strata_touched:
  - D5/S3/Quantum/Tomography/QramCountStatisticInsufficiency
license: citation-only
triage: anchor

Bohac, Bias-Class Discrimination of Universal QRAM Boolean Memories

L. Bohac, arXiv:2512.17503v1 (2025). Quotations are from the v1 TeX source.

A Boolean memory $f:[N]\to \{0,1\}$ with $N=2^n$ is drawn once under a hypothesis and kept fixed; each query returns the address state $|{\psi }_f⟩=N^{-1/2}{\sum }_x(-1{)}^{f(x)}|x⟩$. For the exact-weight class $\mathcal{F}(m)$ with the uniform prior, $t$ queries give the induced state

$${\rho }_p^{(t)}={\mathbb{E}}_{f\sim \mathcal{F}(m)}[(|{\psi }_f⟩⟨{\psi }_f|{)}^{\otimes t}],$$

which need not factor as ${\rho }_p^{\otimes t}$. The separable strategy of Theorem 5.1 measures $\{|+⟩⟨+|,{\Pi }_{\perp }\}$ on each register and tests on the number $k$ of “$+$” outcomes, with $k\sim \mathrm{Binomial}(t,{\mu }^2)$ and $\mu =1-2m/N$. Remark 5.3 states:

An interesting open problem is to characterize the optimal error exponent for distinguishing these exchangeable but potentially correlated mixtures, and to determine whether the “$|+⟩$-count” statistic is sufficient for optimal discrimination in the exact-weight prior model.

Verified locator

Source: https://arxiv.org/abs/2512.17503v1

• DOI: https://doi.org/10.48550/arXiv.2512.17503 (the arXiv-issued DataCite DOI; title, author and year from DataCite; the abstract page lists v1 only).
• URL: https://arxiv.org/abs/2512.17503v1. The e-print member bias_class_discrimination.tex has 570 lines and md5 40312fa46860afbd9a187fe64b700f86. Locations:
  • the persistent-memory model, l. 95 and 255–256; the address state, l. 169–174;
  • exact-weight classes (Definition, $m\in \{0,\dots ,N\}$), l. 244–250;
  • the $t$-copy induced state, l. 397–402;
  • Theorem 5.1 (the count strategy), l. 404–418;
  • Remark 5.3 (the open questions), l. 454–457.