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Zenith Grant Awardee

Bob Coecke

Oxford University


Project Title

A relativistic universe of interacting quantum processes

Project Summary

A game is going on in which two players, Alice and Bob, have an input-output device. They are not supposed to communicate during the game. From the correlations between their inputs and outputs we want to deduce whether they cheated or not. While they may not have been cheating at all, when we film their game and play the movie backwards, now exchanging the roles of inputs and outputs, we may have to conclude that they cheated in this backward reality! A careful analysis of this situation shows that there is nothing mysterious going on, but that the counter-intuitive nature of this example is due to the fact that our intuition with respect to space and time simply doesn't account for probabilities. In this project we want to identify the germ, that causes the above discussed counter-intuitive phenomenon, and explore how it can provide a basis for foundational theories of nature, combining the theories of the very large and the very small.

Technical Abstract

Causal structures, e.g. partial orders, are typically time-symmetric in the sense that each partial ordering trivially yields again a partial ordering under reversal of the order relation. This is not at all the case for quantum processes: while a state can be prepared with certainty, the availability of postselection in a theory (or equivalently, the existence of non-trivial deterministic effects) enables signaling, and hence is in conflict with relativity. So the symmetry present in the space-time structure must break down when unifying it with quantum process structure. The overall goal of this project is to identify the fundamental structure that underpins a universe of quantum relativistic processes, taking time-asymmetry into account in terms of essential aspects of the processes that take place. Important first steps have recently been made by the proposers with the definition of a causal category, which is rich enough to both account for causal structure as well as the basic structures of categorical quantum mechanics, an axiomatic framework for quantum processes built by the proposer and his collaborators in recent years. Since the categories of categorical quantum mechanics consist of generalized relations, the approach proposed above axiomatically substantiates the relational approach to space-time.

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