Contextuality and Wigner negativity are equivalent for continuous-variable quantum measurements

TL;DR

This paper proves that in continuous-variable quantum computing, contextuality and Wigner negativity are fundamentally equivalent resources, unifying two previously distinct concepts crucial for quantum speedup.

Contribution

It establishes the equivalence between contextuality and Wigner negativity in continuous-variable quantum models, providing a unified framework for understanding quantum resources.

Findings

Contextuality and Wigner negativity are equivalent in continuous-variable models.

This equivalence unifies two key quantum resources for speedup.

Results facilitate practical demonstrations of contextuality in continuous variables.

Abstract

Quantum computers will provide considerable speedups with respect to their classical counterparts. However, the identification of the innately quantum features that enable these speedups is challenging. In the continuous-variable setting - a promising paradigm for the realisation of universal, scalable, and fault-tolerant quantum computing - contextuality and Wigner negativity have been perceived as two such distinct resources. Here we show that they are in fact equivalent for the standard models of continuous-variable quantum computing. While our results provide a unifying picture of continuous-variable resources for quantum speedup, they also pave the way towards practical demonstrations of continuous-variable contextuality, and shed light on the significance of negative probabilities in phase-space descriptions of quantum mechanics.