Bias-Class Discrimination of Universal QRAM Boolean Memories
Leonardo Bohac
TL;DR
This work treats Universal QRAM as a fixed, data-independent interface and studies what can be learned about unknown Boolean memories by performing query-based discrimination. By focusing on exact-weight bias classes, the authors show that the induced single-copy ensemble over address states has a two-eigenspace structure, enabling a closed-form Helstrom test and explicit success probability. The analysis yields a clean operational recipe for single-query discrimination and an achievable multi-query strategy under memory persistence, with clear scaling laws and open questions about collective measurements. The results establish a baseline for symmetry-driven information extraction via U-QRAM and provide a bridge to broader quantum-memory discrimination problems, including future work on approximate biases, noise, and genuinely quantum memories.
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.