Violation of Entropic Leggett-Garg Inequality in Nuclear Spins

TL;DR

This paper experimentally demonstrates a violation of the entropic Leggett-Garg inequality in nuclear spins, confirming quantum behavior and challenging macrorealistic theories through NMR experiments.

Contribution

First experimental verification of ELGI violation in a nuclear magnetic resonance system using noninvasive measurements and ancilla qubits.

Findings

ELGI is violated by over four standard deviations in NMR experiments.

Quantum joint probabilities do not reproduce all marginal probabilities.

Results align with quantum theory predictions.

Abstract

We report an experimental study of recently formulated entropic Leggett-Garg inequality (ELGI) by Usha Devi et al. (arXiv: 1208.4491v2 (2012)). This inequality places a bound on the statistical measurement outcomes of dynamical observables describing a macrorealistic system. Such a bound is not necessarily obeyed by quantum systems, and therefore provides an important way to distinguish quantumness from classical behavior. Here we study ELGI using a two-qubit nuclear magnetic resonance system. To perform the noninvasive measurements required for the ELGI study, we prepare the system qubit in a maximally mixed state as well as use the `ideal negative result measurement' procedure with the help of an ancilla qubit. The experimental results show a clear violation of ELGI by over four standard deviations. These results agree with the predictions of quantum theory. The violation of ELGI is attributed to the fact that certain joint probabilities are not legitimate in the quantum scenario, in the sense they do not reproduce all the marginal probabilities. Using a three-qubit system, we experimentally demonstrate that three-time joint probabilities do not reproduce certain two-time marginal probabilities.