A posterior quantum dynamics for a continuous diffusion observation of a coherent channel

TL;DR

This paper derives a quantum filtering equation for continuous diffusion measurement of a coherent channel, showing the system's state relaxes to a coherent state and analyzing the evolution of squeezed states.

Contribution

It introduces a new Belavkin filtering equation for a diffusion observation with a coherent initial state of the measuring apparatus, demonstrating relaxation to a coherent state.

Findings

Filtering equation is relaxing, leading to a coherent state asymptotically.

Time evolution of squeezed states is characterized and compared.

Results extend understanding of quantum trajectories with coherent initial states.

Abstract

We present the Belavkin filtering equation for the intense balanced heterodyne detection in a unitary model of an indirect observation. The measuring apparatus modelled by a Bose field is initially prepared in a coherent state and the observed process is a diffusion one. We prove that this filtering equation is relaxing: any initial square-integrable function tends asymptotically to a coherent state with an amplitude depending on the coupling constant and the initial state of the apparatus. The time-development of a squeezed coherent state is studied and compared with the previous results obtained for the measuring apparatus prepared initially in the vacuum state.