Read-Only Opacity and Restricted-Access Inference on Quantum Memories via U-QRAM

TL;DR

This paper establishes fundamental limitations on read-only access to quantum memories using U-QRAM, showing that coherences are operationally invisible and reducing memory inference to standard state discrimination tasks.

Contribution

It proves that any finite-query protocol's output depends only on the diagonal of the memory in the truth-table basis, revealing a universal restriction on quantum memory access.

Findings

Read-only access factors through dephasing in the truth-table basis.

Memory hypothesis testing reduces to standard state discrimination.

Examples include phase-kickback reduction and indistinguishability of superpositions.

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.