Contextuality, Quantum Computation, and the Church of the Larger Hilbert Space

Joel J. Wallman (University of Waterloo)

Recent research has demonstrated that in many cases, the technological usefulness of quantum mechanical effects is directly related to specific counter-intuitive phenomena. Most notably, it has been shown that contextuality and nonlocality can be quantified as resources in specific models of quantum computation. I will discuss issues that arise when one tries to quantify resources that arise within the standard circuit model of quantum computation and a formal way of quantifying resources based on epsilon nets and a generic simulation framework. In particular, I will argue that resources should be quantified in the pure state formalism only, and that any counter-intuitive phenomena related to the resources should also be framed with respect to the pure state formalism.