Non-locality in theories without the no-restriction hypothesis

Peter Janotta
(Universitaet Wuerzburg)
Raymond Lal
(University of Oxford)

The framework of generalized probabilistic theories (GPT) is a widely-used approach for studying the physical foundations of quantum theory. The standard GPT framework assumes the no-restriction hypothesis, in which the state space of a physical theory determines the set of measurements. However, this assumption is not physically motivated. In Janotta and Lal [Phys. Rev. A 87, 052131 (2013)], it was shown how this assumption can be relaxed, and how such an approach can be used to describe new classes of probabilistic theories. This involves introducing a new, more general, definition of maximal joint state spaces, which we call the generalised maximal tensor product. Here we show that the generalised maximal tensor product recovers the standard maximal tensor product when at least one of the systems in a bipartite scenario obeys the no-restriction hypothesis. We also show that, under certain conditions, relaxing the no-restriction hypothesis for a given state space does not allow for stronger non-locality, although the generalized maximal tensor product may allow new joint states.

In Bob Coecke and Matty Hoban: Proceedings of the 10th International Workshop on Quantum Physics and Logic (QPL 2013), Castelldefels (Barcelona), Spain, 17th to 19th July 2013, Electronic Proceedings in Theoretical Computer Science 171, pp. 84–89.
Published: 27th December 2014.

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