Stabilizer notation for Spekkens' toy theory

TL;DR

This paper introduces a stabilizer notation for Spekkens' toy theory, simplifying calculations and clarifying its similarities and differences with quantum stabilizer states, thereby aiding analysis of states, transformations, and superpositions.

Contribution

It develops a stabilizer notation for Spekkens' toy theory, making its structure more accessible and comparable to quantum stabilizer formalism.

Findings

Facilitates calculations of states and transformations.

Enables definition of superpositions for composite systems.

Clarifies the relationship between the toy theory and quantum stabilizer states.

Abstract

Spekkens has introduced a toy theory [Phys. Rev. A, 75, 032110 (2007)] in order to argue for an epistemic view of quantum states. I describe a notation for the theory (excluding certain joint measurements) which makes its similarities and differences with the quantum mechanics of stabilizer states clear. Given an application of the qubit stabilizer formalism, it is often entirely straightforward to construct an analogous application of the notation to the toy theory. This assists calculations within the toy theory, for example of the number of possible states and transformations, and enables superpositions to be defined for composite systems.