The first measurement of a quantum paradox

How do quantum particles exchange information? An intriguing hypothesis regarding quantum information was recently confirmed by an experimental verification conducted at TU Wien.

If you randomly select an individual from the crowd who is noticeably taller than average, it is very likely that this person will also be above average weight. This is because statistically, knowledge of one variable often gives us some insight into another.

Quantum physics takes these correlations to another level, establishing even more powerful connections between different quantities: individual particles or segments of a vast quantum system can “share” a certain amount of information. This intriguing theoretical premise suggests that the computation of this “mutual information” is surprisingly not affected by the total volume of the system, but only by its surface area.

This surprising result was confirmed experimentally at TU Wien and published in Natural physics. Theoretical contributions to the experiment and its interpretation came from the Max-Planck-Institut für Quantenoptik in Garching, FU Berlin, ETH Zürich and New York University.

Quantum information: More strongly bound than classical physics allows

“Let’s imagine a gas container in which small particles fly around and behave in a very classical way like small spheres,” says Mohammadamin Tajik of the Vienna Center for Quantum Science and Technology (VCQ) — Atominstitut of TU Wien, the first author of the present publication .

“If the system is in equilibrium, then the particles in different regions of the container know nothing about each other. One can consider them completely independent of each other. Therefore, it can be said that the mutual information these two particles share is zero.

In the quantum world, however, things are different: if particles behave quantumly, then it may happen that you can no longer consider them independently of each other. They are mathematically related – you cannot meaningfully describe one particle without saying something about the other.

“For such cases, there has long been a prediction about the mutual information shared between different subsystems of a quantum many-body system,” explains Mohammadamin Tajik. “In such a quantum gas, the shared mutual information is greater than zero and does not depend on the size of the subsystems – only on the outer boundary surface of the subsystem.”

This prediction seems intuitively strange: in the classical world it is different. For example, the information contained in a book depends on its volume, not just the area of ​​the book’s cover. In the quantum world, however, information is often tightly bound to the surface.

Measurements with ultracold atoms

An international research team led by Prof. Jörg Schmidmeier has now confirmed for the first time that mutual information in a many-body quantum system scales with surface area, not volume. For this purpose, they studied a cloud of ultracold atoms.

The particles were cooled to just above absolute zero temperature and held in place by an atom chip. At extremely low temperatures, the quantum properties of particles become increasingly important.

Information spreads more and more throughout the system, and the relationship between individual parts of the overall system becomes more and more significant. In this case, the system can be described by a quantum field theory.

“The experiment is very challenging,” says Jörg Schmidmeier. “We need complete information about our quantum system as far as quantum physics allows. For this purpose, we have developed a special tomographic technique. We get the information we need by perturbing the atoms just a little and then observing the resulting dynamics. It is like throwing a stone into a lake and then getting information about the state of the liquid and the lake from the subsequent waves.

Until the temperature of the system reaches absolute zero (which is impossible), this “shared information” has a limited scope. In quantum physics, this is related to the “coherence length” – it indicates the distance to which particles behave quantumly in a similar way and thus know each other.

“This also explains why shared information does not matter in classical gas,” says Mohammadamin Tajik. “In a classical many-body system, coherence vanishes; you can say that the particles no longer know anything about their neighboring particles. The effect of temperature and coherence length on the mutual information was also confirmed in the experiment.

Quantum information plays an essential role in many technical applications of quantum physics today. The results of the experiment are thus relevant to various research fields, from solid-state physics to the quantum physics study of gravity.

Reference: “Verification of the mutual information area law in a quantum field simulator” by Mohammadamin Tajik, Ivan Kukuljan, Spyros Sotiriadis, Bernhard Rauer, Thomas Schweigler, Federica Cataldini, João Sabino, Frederik Møller, Philipp Schüttelkopf, Si-Cong Ji, Dries Sels, Eugene Demler and Jörg Schmiedmayer, 24 April 2023, Natural physics.
DOI: 10.1038/s41567-023-02027-1