Single Shot Quantum State Estimation via a Continuous Measurement in the Strong Backaction Regime

Abstract

We study quantum tomography based on a stochastic continuous-time measurement record obtained from a probe field collectively interacting with an ensemble of identically prepared systems. In comparison to previous studies, we consider here the case in which the measurement-induced backaction has a nonnegligible effect on the dynamical evolution of the ensemble. We formulate a maximum likelihood estimate for the initial quantum state given only a single instance of the continuous diffusive measurement record. We apply our estimator to the simplest problem -- state tomography of a single pure qubit, which, during the course of the measurement, is also subjected to dynamical control. We identify a regime where the many-body system is well approximated at all times by a separable pure spin coherent state, whose Bloch vector undergoes a conditional stochastic evolution. We simulate the results of our estimator and show that we can achieve close to the upper bound of fidelity set by the optimal POVM. This estimate is compared to, and significantly outperforms, an equivalent estimator that ignores measurement backaction.

arXiv comment10 pages, 5 epic figures

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• On the novelty, efficacy, and significance of weak measurements for quantum tomography
• Near-optimal quantum tomography: estimators and bounds
• Drawing together control landscape and tomography principles
• Volterra filters for quantum estimation and detection
• Characterizing and Quantifying Quantum Chaos with Quantum Tomography
• Quantum state tomography with time-continuous measurements: reconstruction with resource limitations
• Quantum tomography with random diagonal unitary maps and statistical bounds on information generation using random matrix theory
• Tomography of an optomechanical oscillator via parametrically amplified position measurement
• Optimal nonlinear filtering of quantum state
• Loschmidt echo and scrambling of systematic errors in tomography -- a quantum signature of chaos
• Sequential Quantum Measurements and the Instrumental Group Algebra