Qubits, completeness, and contextuality: A new approach to foundations of quantum information

The usual explanation of the quantum computing speedup is parallel calculation, inserting a superposition of all possible input values into the computation. The picture painted is that the machine performs a calculation for every input, perhaps in multiple parallell worlds, and then combines the outcomes of each individual calculation by interference to obtain the desired answer.

This explanation has become standard, but does not give any guidance on how to identify new mathematical problems that could be solved, and how to design algorithms to solve them. New developments seem to need another explanatory model. 

An alternative is tracing the calculation in phase space, a standard tool in classical mechanics but more challenging to use in the quantum realm. The reason is that the Liouville distribution, the probability distribution over classical phase space, becomes the Wigner function in quantum mechanics, a quasi-probability distribution that is not always positive. A negative Wigner function has been linked to presence of quantum
contextuality, a behavior only seen in quantum systems.

This presentation will introduce a description of the phase space of a restriction of quantum mechanics, that generates a positive distribution but still reproduces the contextual behavior of quantum systems. The description is Einstein-complete, but distinct from Bohmian mechanics. We will briefly see how this can be used to give a better explanation of the quantum speedup, but also use this new description as a tool for reasoning about more generic interpretational issues within the foundations of quantum mechanics.