Multiparameter quantum bounds for entanglement-assisted aperture synthesis

RESUMO

Entanglement-assisted optical interferometry promises diffraction-limited imaging over baselines where light cannot be physically combined, but existing theory treats only a single visibility on one two-station baseline. This work formulates the multiparameter estimation problem for an M-station array imaging an extended scene. A reduction lemma shows that the multimode quantum Fisher information (QFI) equals the mean photon number times the QFI of a single delocalized photon, collapsing the problem to a finite-dimensional one. The local photon-number superselection rule (SSR) erases all phase information from the bare state, while shared entanglement restores a fraction f(r)=r/(1+r) of the QFI on a baseline supplied with r pairs -- a factor shown to be achievable, since the reduced two-mode state of any pair is exactly the two-station weak-thermal state. The QFI matrix and its mean Uhlmann curvature reveal numerically that a point source is measurement-compatible, whereas for every extended-source model examined it is incompatible, the Holevo bound exceeding the symmetric-logarithmic-derivative (SLD) bound by up to ~74%. An explicit collective receiver -- a global mode-sorting (quantum Fourier transform) measurement -- then attains a weighted variance within ~7% of the SLD bound and roughly an order of magnitude below an explicit pairwise receiver, and a noisy-resource advantage threshold gives the break-even baseline (~20 km for near-term parameters) beyond which repeater-distributed entanglement beats direct transmission. Finally, the optimal allocation of a finite entanglement budget is a convex program with a closed-form proportional (square-root-law) solution favoring low-visibility baselines. These results recast quantum aperture synthesis as collective multiparameter estimation and give concrete design targets, illustrated on the CHARA array.