Quantum-memory requirement after reference preprocessing

Determine how much quantum memory must be retained after preprocessing quantum references in order to support a subsequent leakage check, including the tradeoff among the number of references, retained memory, ambient dimension, and allowed normal-output tolerance.

Background

The paper establishes an exponential advantage for retaining quantum references coherently rather than converting them into a classical record before processing the message. It also notes that exact compression of identically prepared mixed states can remove maximally mixed Schur-multiplicity registers.

The unresolved issue is the minimum task-specific quantum information that must remain after reference preprocessing to enable the later support test. The authors emphasize that this may require less memory than faithful reconstruction of the entire reference ensemble, and identify reference number, retained memory, ambient dimension, and normal-output tolerance as the relevant tradeoff parameters.

References

A natural next question is how much quantum memory must be retained after reference preprocessing to support the later check. Task-specific compression may retain less information than faithful reconstruction; the tradeoff involves reference number, retained memory, ambient dimension, and normal-output tolerance.

— Exponential Advantage of Quantum over Classical References in Leakage Detection  (2609.36541 - An, 29 Sep 2026) in Discussion section

The joint optimal law as \beta=1-D_0 and \epsilon both vanish is not established here.

— Exponential Advantage of Quantum over Classical References in Leakage Detection  (2609.36541 - An, 29 Sep 2026) in Supplemental Material, Section “Measurement-first estimator and fixed-detection resource law,” paragraph following Eq. (supp:eq:ideal-example)