Contextuality and The Single-Qubit Stabilizer Formalism

TL;DR

This paper reveals that even the simplest quantum systems, like single-qubit stabilizer theory, exhibit generalized contextuality, challenging previous beliefs that such systems are non-contextual and highlighting the complexity of contextuality's role in quantum computation.

Contribution

The study demonstrates that generalized contextuality exists in single-qubit stabilizer theory and clarifies that prepare-and-measure scenarios do not fully capture quantum contextuality.

Findings

Single-qubit stabilizer theory exhibits generalized contextuality.

Contextuality can be confined to transformations within this theory.

Prepare-and-measure scenarios do not fully capture quantum contextuality.

Abstract

Contextuality is a fundamental non-classical property of quantum theory, which has recently been proven to be a key resource for achieving quantum speed-ups in some leading models of quantum computation. However, which of the forms of contextuality, and how much thereof, are required to obtain a speed-up in an arbitrary model of quantum computation remains unclear. In this paper, we show that the relation between contextuality and a compuational advantage is more complicated than previously thought. We achieve this by proving that generalized contextuality is present even within the simplest subset of quantum operations, the so-called single-qubit stabilizer theory, which offers no computational advantage and was previously believed to be completely non-contextual. However, the contextuality of the single-qubit stabilizer theory can be confined to transformations. Therefore our result also demonstrates that the commonly considered prepare-and-measure scenarios (which ignore transformations) do not fully capture the contextuality of quantum theory.