DC 14 – Tensor and polynomial optimisation for quantum information networks

Project Title: Tensor and polynomial optimisation for quantum information networks
Advisors: A. Acin (ICFO), V. Magron (LAAS) Mentor: S. Mansfield (Quandela)
Objectives: We consider quantum communication systems with network of users, corresponding to a network of Hilbert space tensor products, which raises important computational challenges. Different type of correlations will be considered, depending on the different levels of trust and use of the network constraints: 1) Nonlocal Bell correlations: in this scenario, users’ devices are untrusted and no network constraints are enforced. 2) Quantum steering: the devices are different levels of trust, some are fully trusted, others are not. Steering is detected whenever the observer correlations cannot be explained by a hidden-state model. 3) Entanglement: all devices in the network are fully trusted. Entanglement is detected whenever correlations cannot be explained by a separable state. Beyond nonlocality, and with few exceptions, the concepts of 5) network steering 6) network entanglement have hardly been explored. The purpose of this DC is to study all these forms of quantum correlations with no classical analogue and, in particular, design efficient methods for the detection and characterization of correlations in arbitrary networks based on tensor and polynomial optimisation. The optimisation will be handled via different approaches in convex optimisation theory, such as moment-type SDP hierarchies.
Expected Results: Provide more efficient algorithms to detect and characterize quantum correlations in quantum information networks. Writing conference/journal papers and completion of a PhD degree by the DC.
Planned secondment(s): The DC will have a 10 months secondment (M21-30) at LAAS-CNRS to collaborate with V. Magron on exploiting the specific structure of quantum information network to improve the scalability of their quantum correlation detection and characterization. Afterwards, the DC will spend 2 months (M31-M32) at Quandela with S. Mansfield to work on applications to concrete quantum communication networks.
Joint degree: Universitat Politècnica de Catalunya, Paul Sabatier University

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