Quantum filtering for multiple input multiple output systems driven by arbitrary zero-mean jointly Gaussian input fields
This provides a unified framework for quantum filtering in MIMO systems with Gaussian inputs, which is important for quantum optics and quantum information processing.
The paper derives the general quantum filtering equation for MIMO Markovian open quantum systems driven by arbitrary zero-mean jointly Gaussian input fields, extending previous results to include states like vacuum, squeezed vacuum, thermal, and squeezed thermal states.
In this paper, we treat the quantum filtering problem for multiple input multiple output (MIMO) Markovian open quantum systems coupled to multiple boson fields in an arbitrary zero-mean jointly Gaussian state, using the reference probability approach formulated by Bouten and van Handel as a quantum version of a well-known method of the same name from classical nonlinear filtering theory, and exploiting the generalized Araki-Woods representation of Gough. This includes Gaussian field states such as vacuum, squeezed vacuum, thermal, and squeezed thermal states as special cases. The contribution is a derivation of the general quantum filtering equation (or stochastic master equation as they are known in the quantum optics community) in the full MIMO setup for any zero-mean jointy Gaussian input field states, up to some mild rank assumptions on certain matrices relating to the measurement vector.