Quantum Physics

In this talk I am going to describe Spekkens’ toy model, a non-contextual hidden variable model with an epistemic restriction, a constraint on what an observer can know about reality. The aim of the model, developed for continuous and discrete prime degrees of freedom, is to advocate the epistemic view of quantum theory, where quantum states are states of incomplete knowledge about a deeper underlying reality. In spite of its classical flavour, many aspects that were thought to belong only to quantum mechanics can be reproduced in the model. 

I am going to describe our results regarding the formulation of rules for the update of states after measurement. I will do it for systems of discrete prime dimensions and I will then give the idea on how to proceed in the non-prime dimensional case. 

I will also depict the relationship between Spekkens’ model, stabiliser quantum mechanics and Gross' theory of discrete Wigner functions (they are equivalent theories in odd dimensions) in terms of measurement update rules.

I will conclude by briefly discussing a project we have been recently working on that consists of characterising sub theories of Spekkens’ model that are operationally equivalent to sub theories of QM (in particular in the case of qubits) and use them to represent the non-contextual classically simulable part of state-injection schemes of computation with contextuality as a resource.

What is the essence of quantum theory? In the present talk I want to approach this question from a particular operationalist perspective. I take advantage of a recent convergence between operational approaches to quantum theory and axiomatic approaches to quantum field theory. Removing anything special to particular physical models, including underlying notions of space and (crucially) time, what remains is what I shall call "abstract quantum theory". This embeds into a more general framework that also includes classical theory, with classical and quantum theory representing two extremes in a spectrum of possible theories. I shall present this within a "hierarchy of abstraction", where adding structure leads to more specialized frameworks. In particular, adding topological spacetime and locality leads to the recently proposed positive formalism and recovers quantum field theory. Further rigidifying time and adding causality recovers the standard formulation of quantum theory. There are other promising specializations such as Hardy's proposal to work in op-space.