An Introduction to Quantum Filtering

By Luc Bouten, Ramon van Handel, Matthew R. James. SIAM Journal of Control and Optimization, 2006

514 citations recorded by the source corpus.

This paper provides an introduction to quantum filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation as a least squares estimate, and culminating in the construction of Wiener and Poisson processes on the Fock space. We describe the quantum Ito calculus and its use in the modeling of physical systems. We use both reference probability and innovations methods to obtain quantum filtering equations for system-probe models from quantum optics.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/430a30dba95dfa19ce2d89f51f675d15e38fdbe4

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Citations in the corpus

Experimental noise filtering by quantum control (2014, background): “Performance improvement over the desired stopband of the filter captured in cost function A(0W1(W2) 4(8) ) and its di erence relative to that for the primitive operation, A(0Prim 1 ).”
Coherent quantum LQG control (2007, background): “For details on quantum stochastic differential equations and Wiener processes, see [15, 30, 6].”
LQG/H∞ control of linear quantum stochastic systems (2015, background): “The class of linear quantum systems under consideration can be described by using non-commutative or quantum probability theory [14].”
Quantum Feedback Networks: Hamiltonian Formulation (2008, background): “Cascading such systems is a basic example of feedforward [7][11] More generally we can consider feedback connections [21][4][6][14][15][20] [19].”
The Series Product and Its Application to Quantum Feedforward and Feedback Networks (2007, methodology): “We also mention that if an observable of one or more output channels is continuously monitored, then a quantum filter (also called a stochastic master equation) for the conditional density operator can be written down in terms of the parameters ; an example of this is discussed in Section VI-C, see ”
Quantum control theory and applications: A survey (2009, unknown): “required for extracting information from a noisy signal [71].”
Training Schrödinger’s cat: quantum optimal control (2015, methodology): “A promising route is provided by stochastic methods which only require propagation of (several) pure states to unravel the true dynamics [46, 306, 365].”