Connecting tensor networks to quantum causal models with applications to holography
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2023-05
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Master Thesis
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Abstract
Causal modelling aims to describe correlations arising from causal structures providing an information-theoretic notion of causation which is a priori independent on space-time. Conversely, in relativity and quantum field theory, the causal structure is considered to be an essential property of space-time, induced by well-defined light cones. In quantum gravity, space-time cannot be regarded as a fixed classical background and may itself be subject to quantum effects. Therefore, it was suggested that space-time might emerge from many-body quantum correlations. Tensor networks provide a framework to study this hypothesis and allow for a definition of quantum causal influence, which does not assume any pre-defined time slicing. In this work, we propose a connection between the frameworks of causal models and tensor networks which generalises the former and provides an operational meaning to the latter. Our approach is motivated by the similarity between the notions of causal influence in tensor networks and signalling in causal models. Firstly, we generalise quantum causal models in a tensor network-inspired manner and we provide a generalised definition of signalling and interventions. This allows us to define three notions of signalling currently used in literature and show their inequivalence. Then, we provide mappings from tensor networks to causal models and vice versa, showing explicitly a correspondence between signalling and causal influence. Our work lays the foundations for a connection between causal models and tensor networks which would enable an exchange of techniques between the different research fields and could serve as a starting point for novel studies on the emergence of space-time from operational properties of causal models.
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Examiner : Gitton, Victor
Examiner: Mazzola, Giulia
Examiner : Vilasini, Venkatesh
Examiner: Renner, Renato
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ETH Zurich
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Causal models; Tensor networks
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03781 - Renner, Renato / Renner, Renato