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Phase-phenomena in probabilistic theories

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Phase plays a crucial role in many quantum effects including interference. We study phase in probabilistic theories more generally, in order to gain a deeper understanding of phase in quantum theory as well as to consider what could happen in post-quantum scenarios. Phase is normally defined in terms of complex numbers that appear when representing quantum states as complex vectors. Here we give an operational definition whereby phase is instead defined in terms of measurement statistics. The definition makes it possible to ask whether other (convex) probabilistic theories can also have phase and associated phenomena. We use it to explore hypothetical post-quantum particles going through interferometers and find that theories need something like the quantum uncertainty relation between position and unbiased measurements in order to have non-trivial interference, or else they would violate a type of Einstein locality which we dub ‘Branch Locality’. We moreover explore the phase that arises from exchanging particles in scenarios where particles are guaranteed to be indistinguishable but not necessarily quantum. We begin to investigate what new types of particles could exist in such scenarios.

Based on: arXiv:1206.5702, arXiv:1304.5977, arXiv:1307.2529 Joint work with Garner, Murao, Nakata and Vedral.

This talk is part of the CQIF Seminar series.

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