On the epistemic view of quantum states

TL;DR

This paper explores the Spekkens toy model's ability to replicate quantum phenomena, revealing limitations when extending its operations and proposing a correlation test analogous to quantum separability criteria.

Contribution

It formalizes the axioms of Spekkens' toy model, examines the extension of operations, and introduces a correlation test similar to the Horodecki criterion.

Findings

Extended operations form a group isomorphic to the projective extended Clifford Group for two qubits.

Relaxed operations cannot replicate the full Clifford Group, indicating limitations of the toy model.

New correlation tests serve as tools for analyzing entanglement-like correlations in the toy model.

Abstract

We investigate the strengths and limitations of the Spekkens toy model, which is a local hidden variable model that replicates many important properties of quantum dynamics. First, we present a set of five axioms that fully encapsulate Spekkens' toy model. We then test whether these axioms can be extended to capture more quantum phenomena, by allowing operations on epistemic as well as ontic states. We discover that the resulting group of operations is isomorphic to the projective extended Clifford Group for two qubits. This larger group of operations results in a physically unreasonable model; consequently, we claim that a relaxed definition of valid operations in Spekkens' toy model cannot produce an equivalence with the Clifford Group for two qubits. However, the new operations do serve as tests for correlation in a two toy bit model, analogous to the well known Horodecki criterion for the separability of quantum states.