Establish the local-mixing assumptions for concrete quantum rewrites

Establish quantum random-input obfuscation, split-circuit pseudorandomness, and the associated stability assumptions for concrete local functionality-preserving rewrites of ancilla-free quantum circuits, so that the local-mixing framework yields a concrete robust quantum indistinguishability obfuscator.

Background

The paper proves a conditional worst-to-average-case reduction: quantum random-input obfuscation and split-circuit pseudorandomness imply exact channel-preserving qiO for ancilla-free unitary circuits, while an additional stability assumption extends the result to negligibly close channels. These assumptions concern circuit descriptions and correlated side information, not merely black-box access to random unitaries.

No concrete family of local rewrites is shown to satisfy the required assumptions. Establishing them would convert the conditional local-mixing framework into an actual construction of qiO and would provide the concrete foundation needed by the paper’s applications.