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The defence will be in English.
Abstract: There have been recently significant progress in quantum technologies to realize physically diverse quantum computation and simulation platforms. To probe quantum properties associated to entanglement becomes relevant to benchmark and understand the most elementary quantum property generated in these diverse quantum platforms. In this work, we further develop recent theoretical approches based on the randomized measurement (RM) toolbox to probe new fundamental quantities related to entanglement prepared in these quantum devices.
Among the various works done during this thesis, I will firstly focus on providing an effective protocol to measure a fundamental quantity related to quantum metrology known as the quantum Fisher information (QFI) that enables us to characterize multipartite entanglement present in quantum states. This novel protocol is based on estimating the QFI via the RM toolbox, as a converging series of lower bound polynomials of the density matrix beyond the regime of quantum state tomography.
Additionally, we also focus on solving a practical bottleneck of the current RM toolbox caused by the over-burdening classical cost to post-process relevant quantities from experimental RM data. This motivates the introduction of the batch shadow formalism that circumvents this problem and provides an efficient data treatment technique with rigorous performance guarantees to get estimates of quantities accessible from experimental RM data.
Lastly, owing to these developments of the RM toolbox and a collaboration with IBM, we report the first estimation of the QFI for quantum states prepared on IBM superconducting qubit platform by the experimental implementation of this toolbox.
