Simulation security of Scheme II against BPPQNCd adversaries

Prove that the one-time memory scheme II is simulation-secure in the quantum random oracle model against adversaries in the class BPPQNCd for any polynomial depth d.

Background

The paper proves classical-query security for the one-time memory construction using a new sequential POVM bound and conjunction obfuscation, then informally argues that Arora et al.’s lifting framework should extend this result to bounded-depth quantum adversaries. The authors present a formal conjecture stating that their scheme achieves simulation security against BPPQNCd adversaries for any polynomial depth.

A full proof would require adapting the compressed oracle/lifting techniques of Arora et al. to this scheme and showing that depth-bounded quantum adversaries’ oracle interactions effectively reduce to classical transcripts in the required sense, thereby carrying over the classical-query security.