Proportional-subsystem von Neumann concentration for finite-depth optical circuits

Determine whether proportional-subsystem von Neumann entanglement concentration holds for finite-depth passive optical circuit ensembles, including random brickwall networks and more general circuit geometries, as an analogue of the Haar-random interferometer result.

Background

The paper treats Haar-distributed passive interferometers as a maximally randomized benchmark and proves proportional-subsystem weak typicality for the von Neumann entanglement entropy in that ensemble. It notes that finite-depth optical architectures constitute a different and experimentally relevant setting.

The cited work of Shou et al. establishes depth-dependent results for Rényi-2 entropy growth in one-dimensional random brickwall networks and gives separate bounds for average subsystem entanglement and Wasserstein convergence to Haar measure in more general circuit geometries. Whether the corresponding proportional-subsystem von Neumann concentration phenomenon holds for such finite-depth architectures is left unresolved.