Entropic Reciprocity in Time-Reversed Young Interferometry

Abstract

We show that time-reversed Young interferometry reorganizes, rather than reverses, optical entropy. A fixed detector conditions the reciprocal source--detector Green function and produces a source-label probability distribution. Marginal entropies in the standard and time-reversed geometries are generally unequal; the reciprocal invariant is instead the mutual information between source and detector coordinates. Near a destructive response, the conditioned source-label entropy can decrease while Fisher information for small phase, tilt, or defocus perturbations increases. The result identifies time-reversed Young interferometry as a source-space information processor with no analogue in ordinary detector-plane fringe readout.

This work provides an explicit definition on time reversal based on information theory