Operational Approach towards Non-Gaussian States - One Photon at a Time

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Quantum entanglement, one of the key resources for quantum information processing, can be generated in a scalable manner in continuous variable (CV) systems. However such CV entangled states typically display Gaussian statistics, which limits their use for quantum computing. The goal of the present theoretical action is to use techniques from quantum statistical mechanics to design and characterise experimentally realisable non-Gaussian multimode quantum states of light. This task is not only useful for applications in quantum information technologies, but is also relevant from a fundamental physics point of view.Technologies and computing principles must be based on experimentally achievable quantum states. The action focuses on photon-addition or -subtraction applied to multimode quantum states, which is within the reach of state of the art experiments but largely unexplored theoretically. Yet, it opens the door to scalable applications, for instance measurement based quantum computing (MBQC) or tests of quantum supremacy. The action is organised around the following research topics: - Correlations between field quadratures induced by photon-addition and -subtraction.- Experimentally extractable, topological and geometric phase space signatures of photon-addition and -subtraction.- CV-entanglement in photon-added and -subtracted quantum states.- Applications in measurement-based quantum computation and quantum supremacy.The tools developed within these different topics connect mathematical quantum physics with experimental quantum optics to achieve the main goal of the action: to uncover robust characteristics of photon-added and -subtracted Gaussian states, and finally to map these properties to resourcefulness for MBQC.