Frequency tracking and parameter estimation for robust quantum state estimation

In this paper we consider the problem of tracking the state of a quantum system via a continuous weak measurement. If the system Hamiltonian is known precisely, this merely requires integrating the appropriate stochastic master equation. However, even a small error in the assumed Hamiltonian can ren...

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Bibliographic Details
Published in:Physical review. A, Atomic, molecular, and optical physics Vol. 84; no. 5
Main Authors: Ralph, Jason F., Jacobs, Kurt, Hill, Charles D.
Format: Journal Article
Language:English
Published: United States 28.11.2011
Subjects:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
ERRORS
HAMILTONIANS
MATHEMATICAL SOLUTIONS
QUANTUM MECHANICS
QUANTUM STATES
QUBITS
STOCHASTIC PROCESSES
ISSN:1050-2947, 1094-1622
Online Access:Get full text
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Summary:In this paper we consider the problem of tracking the state of a quantum system via a continuous weak measurement. If the system Hamiltonian is known precisely, this merely requires integrating the appropriate stochastic master equation. However, even a small error in the assumed Hamiltonian can render this approach useless. The natural answer to this problem is to include the parameters of the Hamiltonian as part of the estimation problem, and the full Bayesian solution to this task provides a state estimate that is robust against uncertainties. However, this approach requires considerable computational overhead. Here we consider a single qubit in which the Hamiltonian contains a single unknown parameter. We show that classical frequency estimation techniques greatly reduce the computational overhead associated with Bayesian estimation and provide accurate estimates for the qubit frequency.
ISSN:1050-2947
1094-1622
DOI:10.1103/PhysRevA.84.052119