IQC PhD student Hemant Katiyar led the first experiment to violate the Leggett-Garg inequality on a three-level quantum system, demonstrating the possibility of larger violations than previously thought possible.

The Leggett-Garg (LG) test is meant to demonstrate a violation of macrorealism, the idea that macroscopic objects (like cats and tables) cannot exist in superpositions of classically observable states (like dead or alive, here or there), given a certain set of reasonable assumptions. It uses dichotomic, non-invasive measurements to calculate a function with a fixed upper bound for a macrorealistic system and a higher upper bound for a quantum system.

This upper bound is 1 for a macroscopic system, and has long been believed to be 1.5 for a quantum system. However, a recent discovery revealed that this quantum upper bound can be increased up to a maximum of 3 by testing higher dimensional systems than the standard two-level system of the original LG test. The levels of a system are determined by the number of states of the system; for example, a three-level quantum system (qutrit) can exist in three possible states.

Katiyar, along with former IQC postdoctoral fellow Aharon Brodutch (now at the University of Toronto), postdoctoral fellow Dawei Lu, and Executive Director and Canada Research Chair in Quantum Information Raymond Laflamme performed the LG test using nuclear magnetic resonance (NMR). They first created a qutrit out of a macroscopic-sized sample of molecules, chose three distinct times to perform measurements on the system and then performed three independent experiments, starting the system in the same state every time. To accurately estimate the probabilities of the qutrit being in different possible states, they repeated these three experiments many times.

To assure that the violation of the LG inequality is legitimate and not a result of errors, the test requires that the measurements do not disturb the system. Borrowing from IQC associate Sir Anthony Leggett himself, Katiyar explains; “Assume there are two boxes. They’re closed, and there is a ball in either one of them. Now, you open one of the boxes and the ball is not there, so you know it is in the other box. So, in a way, you have measured where the ball is without interacting with the ball.”

The box-ball analogy describes negative result measurement, a method of non-invasive measurement. Even using this method, the researchers had to contend with experimental limitations which disturbed the quantum system. Fortunately, after performing calculations to account for these errors, the violations of the inequality achieved were still greater than the previous theoretical limit.

Perhaps the most gratifying part of the process was consulting with Leggett himself. “He was quite skeptical, I’d say, which is a good thing; being a scientist, he should be. In the end, after telling him how we analyzed our data, we were able to convince him that it was a violation of the LG inequality,” said Katiyar.

Katiyar is quick to elaborate that their results are not a definitive proof that macroscopic realism is false. Though their sample size was macroscopic, it was made up of microscopic molecules, and so a violation of the LG inequality is not unexpected. The importance of their results lies in the use of a three-level system to expand the upper bound beyond what has ever been experimentally achieved, giving a larger buffer for noise and experimental error. Their improvement in the methods of performing an LG test brings researchers one small step closer to violating the inequality with a truly macroscopic object.

The results were published as *Experimental violation of the Leggett-Garg inequality in a 3-level system* in the *New Journal of Physics.*