"Established Connection Between Quantum Theory and Information Theory"

“Established Connection Between Quantum Theory and Information Theory”


# Confirming the Link Between Quantum Complementarity and Entropic Uncertainty: A Milestone by Researchers at Linköping University

Pursuits in quantum mechanics persist in unraveling the enigma of the quantum realm and expanding the limits of human cognition. In an innovative study recently featured in *Science Advances*, a group of scientists from Linköping University in Sweden, in collaboration with partners from Poland and Chile, has experimentally validated a theory that intertwines two crucial principles of quantum mechanics: the **complementarity principle** and **entropic uncertainty**. The findings not only enhance our core comprehension of quantum phenomena but also lay the groundwork for prospective advancements in quantum technology.

“This research is foundational,” states Guilherme B Xavier, a quantum communication expert at Linköping University, Sweden. “Although immediate practical uses are absent, this investigation paves the way for future technological breakthroughs in quantum information and computing. The possibilities for novel discoveries across various domains are vast.”

But what implications does this finding hold, and how does it tie back to our grasp of quantum mechanics? To understand its importance, we must explore the dual concepts that form the basis of the study: the **wave-particle duality** and **entropic uncertainty**.

## Connecting Wave-Particle Duality and the Complementarity Principle

A core yet paradoxical attribute of quantum mechanics is **wave-particle duality**—the concept that quantum entities such as light display both wave-like and particle-like traits. This phenomenon puzzled scientists for centuries and remains a compelling foundation of quantum theory.

The roots of wave-particle duality extend back to the 17th century, when Isaac Newton asserted that light is composed of distinct particles. However, his peers contended that light acted as a wave. The discussion continued until the 19th century, when experiments unveiled the wave-like aspects of light. Yet, in the early 20th century, perspectives shifted once more. Quantum visionaries like Max Planck and Albert Einstein demonstrated that light also possesses features associated with particles, later termed **photons**. Ultimately, in the 1920s, physicist Arthur Compton definitively established that light can embody both wave and particle characteristics, confirming the duality.

This perplexing behavior was clearly defined by Danish physicist **Niels Bohr** through his **complementarity principle**, which asserts that light (and other quantum systems) can appear as either a wave or a particle, but never simultaneously. Importantly, the two behaviors are never entirely independent; their combined properties must remain constant.

## Linking the Complementarity Principle and Entropic Uncertainty

Jump ahead to 2014, when a cohort of scientists in Singapore posited a groundbreaking connection between the complementarity principle and another fundamental concept in quantum theory: **entropic uncertainty**. Entropic uncertainty relates to the level of “unknown” information within a quantum system. It measures the intrinsic limits of our knowledge when observing specific properties of a quantum system, such as energy, position, or momentum.

The Singapore researchers mathematically proved that the wave-particle complementarity of a system also influences its entropic uncertainty. For example, if one seeks to measure the particle-like traits of light, the wave properties become inherently “unknown” and vice versa. Their equations indicated that the total amount of “unknown” information in wave-particle duality is at least one bit—representing the minimal uncertainty arising from the system’s unobservable aspect.

Up until recently, this theoretical link had never been substantiated through experimentation. That’s where the research team from Linköping University made their entry.

## The Pivotal Breakthrough: Experimental Validation and Photon Measurement

Researchers at Linköping University, in conjunction with their global counterparts, have crafted a novel experimental framework to corroborate the Singapore team’s theory. At the heart of their experiment is the utilization of **photons with orbital angular momentum (OAM)**—a specialized type of motion where photons travel in a circular, or twisted, path as opposed to the more typical oscillating (up-and-down) motion. The selection of OAM is crucial, as it enables the system to encode additional information and boosts its potential for real-world applications in quantum communication.

The experiment employs an **interferometer**, a device widely used in quantum physics to examine wave-particle interactions. In this configuration, photons are directed towards a **beam splitter**, causing their paths to diverge and then recombine at a second beam splitter. The clever twist is that the second beam splitter can be **partially inserted** by researchers, allowing them to measure the photons’ properties as waves, particles, or a combination of both—something traditional arrangements are unable to accomplish.

This groundbreaking experimental arrangement permitted researchers to observe and validate the entropic uncertainty relationship concerning wave-particle duality. Their findings demonstrated that regardless of how the complementarity between wave and particle features is distributed, the total uncertainty in the system always adher