Physicists use the light spectrum in 37 dimensions to prove the quantum paradox

A game with only three moves may sound simple. In quantum physics, it can still break old logic.

That is the focus of a new experiment led by physicist Zhenghao Liu and his colleagues at the Technical University of Denmark. Writing in Science Advances, the team has constructed what they describe as the Greenberger-Horne-Zeilinger triple factor, or GHZ model, which is amazing. Then they presented its statistics in the form of a 37-dimensional optical system. As a result, the result strengthened one of the most surprising claims of quantum theory: what you can say about a system depends on how you choose to measure it.

In ordinary life, measurement seems to be meaningless. You check speed, mass, temperature, and assume that the object you measured already has that value. However, quantum mechanics does not allow you to keep that image. This study focuses on context, the idea that even if the measurements are consistent, you still cannot assign fixed preexisting values ​​without specifying the full meaning of the measurement.

The GHZ conflict has always served as one of the cleanest ways to expose that tension. It creates a situation where quantum theory and any other hidden model make predictions that clearly conflict. In other words, they don’t just clash in numbers.

Liu’s group asked a fundamental but unsolved question: what minimum level of measurement is needed to cover all GHZ-type phenomena?

Their answer was three. The team showed that a three-level cover is possible and also proved that the number cannot be reduced further. According to the paper, popular models of the GHZ model required at least four levels. Meanwhile, one or two are not accepted in theory.

That made the result more than just cleaning up the numbers. The researchers argue that the weak coverage of the context corresponds to a stronger type of anomaly and a larger quantum-classical ratio. This ratio emerges when chaos is transformed into a testable inequality.

To achieve that level, they used graph theory. In their design, measurement events become vertices in a discrete graph, and incommensurate events are connected by graph properties such as independence number, Lovász number, and chromatic number. Using that method, the team identified a candidate structure based on the complement of the Perkel graph. Then they created a clear version of the GHZ model from it.

The final construction required measurements in 37-dimensional Hilbert space.

That high level presented a testing challenge. Instead of using a very cumbersome multiqubit platform, the researchers switched to photons and equipped the system with a time-bin degree of freedom of integrated light.

Their setup used a pulsed fiber laser, an intensity and phase modulator, a fiber ring that did optical convolution, and homodyne detection. The 37-dimensional world is divided into six specific general areas. Each subspace was handled in different ways. Homodyne detection enables the team to regain the height information needed to reconstruct the correct measurement methods.

The appeal of that design was scalability. The authors stated that seeing the full amplitude and phase data allowed them to expand the available Hilbert space significantly. In fact, the devices ran at a locking speed of 10 kilohertz. In addition, the stability of the active phase captured the optical parameters during the measurement.

The test also tested whether the supposedly unique events actually behaved as they did within the devices. For pairs of rays and specific projectors, the average probability of detection was only 1.74 (11)%. The researchers took this as evidence of high orthogonality at the stage of preparation and measurement.

When the team estimated three probabilities that describe the disorder, the data were consistent with statistical predictions and strongly contradicted non-statistical models.

Then they moved on. Because perfect orthogonality is never achieved in a real experiment, the authors also tested for inequality related to noncontextuality, which corrects for imperfect selection. After that adjustment, the data was still crossing the highs that did not match the 8.06 range.

That gave the study two levels of power. It produced a complex GHZ model with very low-level coverage, and demonstrated that a high-performance optical platform can accurately reproduce the required structure to reject inconsistencies.

The result did not come without caveats.

The authors state that their current setting does not produce random event results, meaning it is not a randomized controlled trial. They also found opportunities that violate the inequality of status, but those opportunities are not as well defined as a different hypothesis would require. Furthermore, they note that part of the quantum of probability depends on quantum theory itself. According to the paper, replacing the final measurement with photodetection can solve both problems in the latter work.

This research gives physicists a clean way to study some of the most powerful connections in quantum theory. It also points to a flexible optical platform for probing advanced quantum systems without relying on a large number of detectors.

The authors suggest that a similar approach may help search for other unusual relationships. It can also support work in the shallow quantum circuit and connect to existing platforms based on quantum computing and Gaussian boson sampling.

Importantly, the study reduces the old theoretical question by showing that the three dimensions of the context are sufficient, and that no small structure can work.