Gebhart, Valentin (2021) Quantum Resources in Quantum Technologies: Identification, Verification, and Application. [Tesi di dottorato]

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Abstract

Quantum technologies employ the laws and phenomena of quantum mechanics to address different tasks in various technological fields such as, e.g., computation, cryptography, or sensing. Specific quantum features empower quantum technologies to achieve technological advantages over classical technologies. These features are often called quantum resources. In this thesis, we study quantum resources from different viewpoints. We delve into the identification of the central quantum resources in quantum computation, we address the verification of specific quantum resources from experimental data, and we apply quantum resources to develop new quantum technologies. The crucial quantum resources that enable a quantum advantage of quantum computers over classical ones for specific computational problems have been intriguing scientists since the introduction of quantum computation. We focus on a specific quantum algorithm, Grover's algorithm, and examine quantum resources that are necessary for its computational advantage over classical technologies. We find that the maximal trace speed of the quantum state during the algorithm can be used to bound the quantum advantage in different noisy versions of Grover's algorithm. The trace speed can be interpreted as a measure of the quantum resources of coherence or entanglement. Verifying the presence of a certain quantum resource in an experimental setup is generally a difficult problem and requires specific techniques and strategies that depend on the quantum resource in question. For instance, the verification of the quantum resource of Bell nonlocality requires violations of Bell inequalities. These violations can be forged by means of the selection bias if the observed data are postselected collaboratively by the different experimental parties. We prove conditions for partially-collaborative postselection strategies that are valid for the verification of genuine multipartite nonlocality. In the field of continuous-variable quantum technologies, a central quantum resource is nonclassicality. The verification of nonclassicality is generally cumbersome and requires large amounts of experimental data. We develop and train neural-network-based nonclassicality indicators that predict nonclassicality directly from small amounts of experimental data produced in different standard quantum-optical measurement schemes. The method is applied to real experimental data from homodyne measurements. Finally, we employ the toolbox of quantum mechanics to develop a quantum algorithm that performs Bayesian multiphase estimation at the optimal precision scaling, where we take into account all physical resources that are used in the estimation protocol. The algorithm can be implemented in state-of-the-art quantum optical architectures and represents a potential subroutine for technologies in quantum sensing and quantum computation.

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