Entropic Reciprocity in Time-Reversed Young Interferometry

TL;DR

This paper demonstrates that time-reversed Young interferometry reorganizes optical entropy, revealing an invariant mutual information and unique information processing capabilities not present in standard interferometry.

Contribution

It introduces the concept that time-reversed Young interferometry reorganizes entropy and identifies mutual information as an invariant, offering new insights into optical information processing.

Findings

Mutual information between source and detector is invariant under time reversal.

Near destructive interference, source-label entropy can decrease while Fisher information increases.

Time-reversed Young interferometry acts as a source-space information processor.

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.