Read-Only Opacity and Restricted-Access Inference on Quantum Memories via U-QRAM
Leonardo Bohac
TL;DR
The paper investigates what can be learned about a quantum memory via a fixed, data-independent U-QRAM read interface when the memory register is inaccessible. It proves a protocol-independent read-only opacity theorem: the accessible output depends only on the memory's diagonal in the truth-table basis, equivalently the read-out map is entanglement-breaking and coherences between truth tables are invisible. This reduces memory-hypothesis discrimination to Helstrom-optimal discrimination on induced accessible states, and the authors illustrate with a phase-kickback geometry, a minimal 3/4 success example, and indistinguishability of relative phases in entangled memories. The results clarify fundamental limits of noninvasive memory inference and provide a foundation for analyzing or designing fixed-interface quantum memories in quantum information processing.
Abstract
Universal QRAM (U-QRAM) is a fixed, data-independent unitary interface that implements coherent random-access reads relative to a designated computational "truth-table" basis on the memory register. This work studies restricted-access inference: the memory register is persistent but inaccessible, while an experimenter may prepare and measure only accessible registers and may invoke the fixed read interaction. Allowing the memory to be in an arbitrary quantum state (pure or mixed, possibly entangled with an inaccessible reference system, or a coherent superposition of truth tables), we establish a sharp, protocol-independent limitation of read-only access. For any finite-query protocol -- including arbitrary accessible ancillas, intermediate measurements, adaptivity, and general CPTP processing between queries -- the induced output state on the accessible registers depends on the memory state only through its diagonal in the truth-table basis. Equivalently, read-only access factors through dephasing (pinching) in that basis; coherences between distinct truth tables are operationally invisible. Consequently, every memory-hypothesis testing task reduces to a standard state-discrimination problem on the accessible registers, and the minimum-error optimal measurement is characterized by Helstrom theory. We illustrate the framework with three explicit examples: (i) the phase-kickback reduction recovering the one-query Bernstein-Vazirani/Deutsch-Jozsa geometry, (ii) a minimal Helstrom instance with optimal success probability 3/4, and (iii) perfect indistinguishability of relative phases in entangled truth-table superpositions.