Dynamics, switching, and the unitary model

The formal white-noise interaction has not been treated as a bounded Hamiltonian. Its well-defined unitary model is the one-particle map just proved and its second quantization. Accordingly, no finite-dimensional Hamiltonian norm estimate is applied to this unbounded bosonic capture evolution.

The storage attenuation is an ordinary vacuum beam-splitter channel with transmissivity $e^{-{\kappa }_s{T}_s}$; it can be defined by the same passive dilation. With the initial memory replaced by vacuum, capture and storage together are vacuum pure loss of transmissivity ${\tau }_{\ast }$ on the selected port mode.