Certifying the quantumness of a nuclear spin qudit through its uniform precession

TL;DR

This paper demonstrates the quantumness of a nuclear spin qudit through uniform precession by measuring positivity of its spin projection, using a high-spin nucleus to violate classical bounds and certify quantum states.

Contribution

It introduces a method to certify quantum behavior in a nuclear spin qudit by measuring positivity, surpassing classical explanations, and uses high-fidelity quantum state preparation and measurement.

Findings

Violates classical bounds by 19 standard deviations

Successfully prepares and measures quantum resource states in a single atomic-scale qudit

Demonstrates the quantumness of nuclear spin precession beyond classical models

Abstract

Spin precession is a textbook example of dynamics of a quantum system that exactly mimics its classical counterpart. Here we challenge this view by certifying the quantumness of exotic states of a nuclear spin through its uniform precession. The key to this result is measuring the positivity, instead of the expectation value, of the $x$-projection of the precessing spin, and using a spin > 1/2 qudit, that is not restricted to semi-classical spin coherent states. The experiment is performed on a single spin-7/2 $^{123}$Sb nucleus, implanted in a silicon nanoelectronic device, amenable to high-fidelity preparation, control, and projective single-shot readout. Using Schr\"odinger cat states and other bespoke states of the nucleus, we violate the classical bound by 19 standard deviations, proving that no classical probability distribution can explain the statistic of this spin precession, and highlighting our ability to prepare quantum resource states with high fidelity in a single atomic-scale qudit.