Bias-Class Discrimination of Universal QRAM Boolean Memories

• URL: http://arxiv.org/abs/2512.17503v1
• Date: Fri, 19 Dec 2025 12:14:18 GMT
• Title: Bias-Class Discrimination of Universal QRAM Boolean Memories
• Abstract summary: Given query access to a quantum memory, we ask: what can be inferred about the bias class of $f$ using coherent, addressable queries?<n>We show that for exact-weight bias classes, the induced single-query ensemble state on the address register has a two-eigenspace structure that yields closed-form expressions for the single-copy Helstrom-equivalent measurement and success probability.<n>This goes beyond the perfect-discrimination case of Deutsch-Jozsa and complements exact-identification settings such as Bernstein-Vazirani.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the discrimination of Boolean memory configurations via a fixed Universal QRAM (U-QRAM) interface. Given query access to a quantum memory storing an unknown Boolean function $f:[N]\to\{0,1\}$, we ask: what can be inferred about the bias class of $f$ (its imbalance from $1/2$, up to complement symmetry) using coherent, addressable queries? We show that for exact-weight bias classes, the induced single-query ensemble state on the address register has a two-eigenspace structure that yields closed-form expressions for the single-copy Helstrom-optimal measurement and success probability. Because complementing $f$ changes the state $|ψ\rangle$ only by a global phase, hypotheses $p$ and $1-p$ are information-theoretically identical in this model; thus the natural discriminand is the phase-bias magnitude $|μ|$ (equivalently $μ^2$). This goes beyond the perfect-discrimination case of Deutsch-Jozsa and complements exact-identification settings such as Bernstein-Vazirani.

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