Contextuality and Wigner Negativity Are Equivalent for Continuous-Variable Quantum Measurements

Quantum computers promise 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 realization 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 toward practical demonstrations of continuous-variable contextuality and shed light on the significance of negative probabilities in phase-space descriptions of quantum mechanics.

Figure 1

Experimental protocol corresponding to the quadrature measurement scenario ${⟨\mathcal{X},\mathcal{M},\mathcal{O}⟩}_{\mathrm{quad}}$.