Locally Scrambled Quantum Memories for Loss-Tolerant Entanglement-Assisted Optical Interferometry

We formulate a loss-tolerant extension of entanglement-assisted long-baseline optical interferometry in which the astronomical optical coherence is first mapped coherently to distributed quantum memories and is subsequently protected by local scrambling encoders. The proposal must be distinguished from existing memory-assisted Gottesman--Jennewein--Croke (GJC) interferometers, in which quantum memories store an ancillary single-photon-entangled reference rather than the astronomical state itself. We derive the weak-thermal-light model, its two-parameter quantum Fisher information (QFI) matrix, the GJC measurement probabilities, and the associated classical Fisher information (CFI). We then prove that exact local correction of flagged erasures restores the complete complex visibility, its QFI matrix, and the operational GJC CFI. The relevant protection criterion is reference--environment decoupling, not volume-law entanglement alone. We state, as conjectures, quantitative decoupling bounds for local random encoders and finite-depth scramblers, and derive the expected threshold of fewer than one half of the physical memories erased per node. Finally, we formulate the phase-covariance and superselection-rule constraints required for a physically meaningful distributed protocol.