Quantum state tomography with noninstantaneous measurements, imperfections, and decoherence

Pierre Six 1, 2 Philippe Campagne-Ibarcq 2, 3 Igor Dotsenko 4 Alain Sarlette 2 Benjamin Huard 3 Pierre Rouchon 2, 1
2 QUANTIC - QUANTum Information Circuits
ENS Paris - École normale supérieure - Paris, UPMC - Université Pierre et Marie Curie - Paris 6, MINES ParisTech - École nationale supérieure des mines de Paris, Inria de Paris
Abstract : Tomography of a quantum state is usually based on a positive-operator-valued measure (POVM) and on their experimental statistics. Among the available reconstructions, the maximum-likelihood (MaxLike) technique is an efficient one. We propose an extension of this technique when the measurement process cannot be simply described by an instantaneous POVM. Instead, the tomography relies on a set of quantum trajectories and their measurement records. This model includes the fact that, in practice, each measurement could be corrupted by imperfections and decoherence, and could also be associated with the record of continuous-time signals over a finite amount of time. The goal is then to retrieve the quantum state that was present at the start of this measurement process. The proposed extension relies on an explicit expression of the likelihood function via the effective matrices appearing in quantum smoothing and solutions of the adjoint quantum filter. It allows us to retrieve the initial quantum state as in standard MaxLike tomography, but where the traditional POVM operators are replaced by more general ones that depend on the measurement record of each trajectory. It also provides, aside from the MaxLike estimate of the quantum state, confidence intervals for any observable. Such confidence intervals are derived, as the MaxLike estimate, from an asymptotic expansion of multidimensional Laplace integrals appearing in Bayesian mean estimation. A validation is performed on two sets of experimental data: photon(s) trapped in a microwave cavity subject to quantum nondemolition measurements relying on Rydberg atoms, and heterodyne fluorescence measurements of a superconducting qubit.
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Contributor : Alain Sarlette <>
Submitted on : Friday, November 11, 2016 - 12:47:12 AM
Last modification on : Tuesday, May 14, 2019 - 10:40:26 AM
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Pierre Six, Philippe Campagne-Ibarcq, Igor Dotsenko, Alain Sarlette, Benjamin Huard, et al.. Quantum state tomography with noninstantaneous measurements, imperfections, and decoherence. Physical Review A, American Physical Society, 2016, 93, pp.12109. ⟨10.1103/PhysRevA.93.012109⟩. ⟨hal-01395584⟩

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