Volterra filters for quantum estimation and detection
arXiv:1509.02133 · doi:10.1103/PhysRevA.92.062119
Abstract
The implementation of optimal statistical inference protocols for high-dimensional quantum systems is often computationally expensive. To avoid the difficulties associated with optimal techniques, here I propose an alternative approach to quantum estimation and detection based on Volterra filters. Volterra filters have a clear hierarchy of computational complexities and performances, depend only on finite-order correlation functions, and are applicable to systems with no simple Markovian model. These features make Volterra filters appealing alternatives to optimal nonlinear protocols for the inference and control of complex quantum systems. Applications of the first-order Volterra filter to continuous-time quantum filtering, the derivation of a Heisenberg-picture uncertainty relation, quantum state tomography, and qubit readout are discussed.
v2: added more in-depth discussions, more references, and a qubit readout example with two new figures. Improved presentation; v3: extended and published
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Cited by in corpus (7)
- Real-Time Kalman Filter: Cooling of an Optically Levitated Nanoparticle
- Rapid estimation of drifting parameters in continuously measured quantum systems
- A Quantum Extended Kalman Filter
- Continuous quantum error correction for evolution under time-dependent Hamiltonians
- Estimation of parameters in circuit QED by continuous quantum measurement
- Practical Trainable Temporal Postprocessor for Multistate Quantum Measurement
- An Improved Quantum Projection Filter