Bias-Class Discrimination of Universal QRAM Boolean Memories
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914210274869248 |
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| author | Bohac, Leonardo |
| author_facet | Bohac, Leonardo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17503 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bias-Class Discrimination of Universal QRAM Boolean Memories Bohac, Leonardo Quantum Physics 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. |
| title | Bias-Class Discrimination of Universal QRAM Boolean Memories |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.17503 |