Experimental demonstration of quantum advantage in communication complexity for Euclidean distance problem

When considering the complexity of communication protocols, the aim is to perform a certain task with the minimum amount of communication resources, such as time and transmitted information. The new analysis still awaits peer review, but it already lays out the central claim clearly.

It matters because physics only takes a result seriously when the measurement chain remains robust under scrutiny. Experimental particle physics and precision metrology both operate in regimes where the signal sits far below the background noise, and where systematic uncertainties can mimic new physics if not controlled rigorously. The history of the field contains numerous anomalies that generated theoretical excitement before better data showed them to be artifacts, and it also contains genuine discoveries that were initially dismissed as noise. The difference is almost always resolved by independent replication with different instruments and different systematics. The use of quantum states may lead to an exponential advantage in the use of such resources. Here, we are interested in the task of calculating the Euclidean distance between two vectors representing real data sets.

It has been previously shown that it is possible to obtain an advantage for this task based on quantum fingerprinting. We perform a proof-of-principle experimental demonstration of the Euclidean distance protocol using amplitude modulation techniques for encoding non-binary data sets and.

We show a quantum advantage in transmitted information surpassing the best classical protocol for an input size of $10^8$, for diverse types of data sets, including those. Our results highlight the potential of quantum communication complexity for use in a broad set of applications.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. ArXiv is committed to these values and only works with partners that adhere to them.

The broader interest lies as much in the method as in the headline number, because a durable measurement procedure can travel farther than a single result. When experimental physicists develop a technique that achieves new sensitivity or controls a previously uncharacterized systematic, that methodological contribution persists even if the specific measurement is later revised. This is one reason why precision physics experiments often generate long-term value that is not immediately visible in the original publication.

Have an idea for a project that will add value for arXiv's community.

Because this is still a preprint, the result should be read with genuine interest and proportionate caution. Peer review is not a guarantee of correctness, but it is a process that forces authors to respond to technical criticism from specialists who have no stake in a particular outcome. Preprints that survive that process, often with substantive revisions, emerge with a stronger evidential base than the version that first appeared. Until that stage is complete, the responsible reading keeps uncertainty explicitly visible rather than treating the claims as established findings.

The next step is more measurement, tighter systematic control and scrutiny from groups whose experimental setups are genuinely independent. In experimental particle physics and precision metrology, the threshold for a discovery claim is a five-sigma excess surviving multiple analyses; an intriguing signal at lower significance is a reason to run more experiments, not a reason to revise the textbooks. Next-generation experiments currently under construction or commissioning will revisit several of the open questions that give the current result its context. Until peer review and independent follow-up address those open questions, skepticism is not a failure of appreciation for the work; it is part of how science decides what to keep.

Source