*AsianScientist (Dec. 24, 2014)* – Using novel techniques from information theory, researchers from the National University of Singapore have demonstrated a striking and fundamental relationship between two fundamental characteristics of quantum physics—wave-particle duality and the uncertainty principle. This research, published in *Nature Communications*, paves the way for more elegant tests of both phenomena in quantum systems.

“We were looking for connections between wave-particle duality and the uncertainty principle, which appear on the surface to be completely different properties of a quantum system,” explained Dr. Patrick Coles, one of the physicists behind the breakthrough.

The uncertainty principle states that certain pairs of “complementary” quantities cannot be simultaneously measured to arbitrary accuracy. Most famously, the more accurately one measures a particle’s position, the less accurately one can measure its momentum—a counterintuitive notion that even Einstein famously argued against.

On the other hand, wave-particle duality states that quantum objects can display particle-like or wave-like behavior. In particular, researchers routinely measure the interference patterns that result when waves are superimposed on each other, and wave-particle duality states that the stronger these patterns are the weaker particle observations (such as having a specific location in space) must be.

“However, notice that you can talk about wave behavior without ever mentioning uncertainty,” said Coles, “and a lot of wave-particle predictions are made on a case-by-case basis, because there isn’t a unifying framework for predicting what particle or wave behavior looks like in any particular experiment.”

To see a connection with the uncertainty principle, the researchers therefore had to translate the language of wave and particle behavior into the language of uncertainty. They did this by working out how to write down wave and particle behavior each as an experimenter’s knowledge of a particular physical observable.

It turned out that when they did so, the observables they had written down were precisely related in a way through “entropic uncertainty relations”, which are re-statements of the uncertainty principle that use information theory to describe knowledge of physical observables.

“It was like finding the Rosetta Stone that allowed us to translate unfamiliar hieroglyphics—the literature on wave-particle duality—into the much more familiar language of entropic uncertainty relations,” Coles told

Asian Scientist Magazine.“We were excited because these concepts had never been translated in this way before. So we had a lot of fun going through each article in the wave-particle duality literature and translating each one, and also showed how future experiments might be translated in a similar way.”

These findings not only reveal how two seemingly unrelated quantum mysteries are in fact intimately connected, but may already have practical implications. Entropic uncertainty relations are already being applied in some practical aspects of quantum cryptography, as such the researchers’ results may inspire new quantum cryptographic protocols that exploit the wave-particle duality of light effectively to encrypt and secure messages.

The researchers had previously discovered striking connections between the uncertainty principle and other physics, such as quantum non-locality and the second law of thermodynamics and this new result is prompts further research into how all these different aspects of nature might be fundamentally related.

The article can be found at: Coles et al. (2014) Equivalence of Wave–Particle Duality to Entropic Uncertainty.

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Copyright: Asian Scientist Magazine; Photo: National University of Singapore.

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