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Overall Objectives
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Overall Objectives
Application Domains
Bibliography


Section: New Results

Quantum state tomography with non-instantaneous measurements, imperfections, and decoherence

Participants: Pierre Six, Alain Sarlette, Benjamin Huard, Pierre Rouchon

Tomography of a quantum state is usually based on 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 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 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 multi-dimensional Laplace integrals appearing in Bayesian Mean estimation. This work should allow much more accurate inference of the state achieved by some quantum experiment, before a non-instantaneous measurement process is performed to check its results – distinguishing the loss in fidelity truly incurred by the preparation process, from the loss in fidelity induced only by the benchmarking measurement process which would not be present in the final application. A validation is performed on two sets of experimental data: photon(s) trapped in a microwave cavity subject to quantum non-demolition measurements relying on Rydberg atoms, where we have collaborated with the group of Igor Dotsenko at the LKB, College de France; and the heterodyne fluorescence measurements of a superconducting qubit, with the experimentalists of the QUANTIC team.

This result has been published in [27].