Abstract
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 jointly Gaussian input field states, up to some mild rank assumptions on certain matrices relating to the measurement vector.
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Dedicated to the memory of Slava Belavkin
Research supported by the Australian Research Council
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Nurdin, H.I. Quantum filtering for multiple input multiple output systems driven by arbitrary zero-mean jointly Gaussian input fields. Russ. J. Math. Phys. 21, 386–398 (2014). https://doi.org/10.1134/S106192081403011X
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DOI: https://doi.org/10.1134/S106192081403011X