In a future where quantum technologies are more common, certifying that devices have truly quantum components, and that correlations are quantum (rather than of classical origin), will be important.
But tests of the quantum nature of physical systems (their non-classicality) are complicated by the requirement of randomness in the inputs to such tests. For example, the true randomness that quantum systems are known to exhibit can be certified only in a device-independent manner, by an experiment that in turn needs true randomness in the inputs. At least qualitatively, this argument is circular.
In 2023, EQUS researchers from the Qudits@UQ laboratory—led by Chief Investigator Jacqui Romero—developed a way of determining whether observed correlations can be explained by classical physics, without the requirement of randomness.
Certifying non-classicality without requiring randomness
Traditional experimental tests usually require a random string of bits. Although this requirement sounds simple enough, it’s actually hard to come by—for example, random numbers produced by a computer are only pseudo-random. The team’s experiment does away with this challenging requirement by framing the test in terms of a game1.
In this context, they showed that quantum correlations have a clear advantage over classical correlations: the correlations obtained from entangled photons cannot be replicated using two two-level classically correlated entities. As such, they provide a proof of concept—the only one of its kind—for certifying non-classicality from only the output statistics and operational dimension of the device, without the need for true randomness.
Quantum advantage via a toy game
In the game frame, two entangled photons are generated. One is sent to player A (Alice) and the other to player B (Bob). Alice and Bob then measure the ‘shape’ of their photon, and the team record the outcomes. The team have previously calculated the probabilities of obtaining certain outcomes, to compare with the observations.
As an example, consider two two-level photons, which may be either ‘squares’ or ‘circles’ with equal probability. If the photons behaved classically, Alice would expect to find a square half the time and a circle half the time, as would Bob. In addition, Alice and Bob should both find squares 25% of the time, both find circles 25% of the time, and find different shapes (one a circle, the other a square) 50% of the time. If the photons are truly entangled (truly quantum), then Alice would still expect to find a square half the time and a circle half the time, as would Bob. However, Alice and Bob will always find the same shape—both find squares 50% of the time and both find circles 50% of the time.
This ‘shared’ or correlated randomness challenges classical notions of randomness and is a direct consequence of quantum entanglement. Therefore, by comparing the expected and observed shared outcomes of the game, the team can determine the ‘quantumness’ of the photons.
Importantly, there is no way to rig the game, for example, by ‘weighting’ the photons (making them squares only 30% of the time and circles 70% of the time). Therefore, whether the photons behave truly randomly or not is irrelevant—the shared randomness distribution will always reveal the nature of the system.
The game also works for higher-level photons (more possible photon ‘shapes’), provided the team know the number of options in advance so they can calculate the probabilities of the expected shared outcomes.
The future for shared randomness
The team used the entanglement of the transverse spatial mode of photons generated in a nonlinear crystal using spontaneous parametric downconversion. This method could help to scale up photonic entangled systems (whether in free space or on-chip) for future quantum networks. In 2024, the team will re-build the entangled photon source and measurement apparatus for this experiment to improve the quality (fidelity) of the high-dimensional entangled states.
Because the proof of concept relies on knowing the operational dimension of the device, the test is still semi-device-dependent. In the longer term, the team hope to explore the possibility of making quantum advantage device-independent and demonstrating it experimentally.
Shared (or correlated) randomness is a useful resource for many tasks, so the results have implications for quantum information processing more broadly. For example, quantum communication protocols, such as certain secret-sharing schemes or quantum computations that involve a randomness distribution component (which has been shown to enhance security), may benefit from the team’s results.
This story was first published in the 2023 EQUS annual report, and was written by Kristen Harley.