Quantum Networks in Space-Time

Quantum theory usually assumes that the order in which events occur is fixed: given two events A and B, either A is in the causal past of B, A is in the causal future of B, or A and B are causally disconnected.

This suggests some intriguing questions: What happens if we apply the laws of quantum mechanics to the causal order itself? Can we describe quantum physics when the usual notion of a causal structure becomes “fuzzy”? What kind of phenomena and information processing features can we expect in this scenario?

Such questions are likely to be relevant for the phenomena expected in a theory of quantum gravity, and for the information theoretic power of such a theory.

Recently, physicists working on quantum foundations have developed compositional frameworks for quantum mechanics on indefinite causal structures, starting to shed light on these questions.

Up to now, the frameworks rely on abstract Hilbert space constructions, and there is no clear connection between this approach and other approaches to space-time physics. The goal of the present proposal is to make such a connection.

Specifically, QuNeS will 1) Formulate an operational and compositional framework for quantum theory with indefinite causal structure where a notion of space-time appears explicitly.

The formulation will include a detailed understanding of the symmetries of space-time quantum networks, and the treatment of quantum fields as systems under study. 2) Explore information-theoretic advantages implied by the framework. 3) Study the realization of indefinite causal structures.

This study will include the possible gravitational origin of the realization, for example through the entanglement of gravitating quantum clocks.

QuNeS will combine the researcher's experience on quantum clocks and dynamics of causal structures together with the host's expertise in compositional quantum theory and quantum foundations to reach a deeper understanding of causality and locality in quantum mechanics.