Some things are related, others are not. Suppose you randomly select a person from a crowd who is significantly taller than the average. In that case, there is a good chance that they will also weigh more than the average. Statistically, one quantity also contains some information about the other. Quantum physics allows for even stronger links between different quan­tities: different particles or parts of an extensive quantum system can share a certain amount of information. There are curious theoretical predictions about this: sur­prisingly, the measure of this mutual information does not depend on the size of the system but only on its surface. This surprising result has been confirmed experimentally at the TU Wien. Theoretical input to the experiment and its inter­pretation came from the Max-Planck-Institut für Quanten­optik in Garching, FU Berlin, ETH Zürich and  New York University.

“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). “If the system is in equilibrium, then particles in different areas of the container know nothing about each other. One can consider them completely inde­pendent of each other. Therefore, one can say 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 connected – you can't 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 many-body quantum system,” explains Mohamma­damin Tajik. “In such a quantum gas, the shared mutual information is larger than zero, and it does not depend on the size of the subsystems – but only on the outer bounding 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 merely on the area of the book's cover. In the quantum world, however, information is often closely linked to surface area.

The international research team led by Jörg Schmiedmayer has confirmed for the first time that the mutual information in a many body quantum system scales with the surface area rather than with the 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 the particles become increasingly important. The infor­mation spreads out more and more in the system, and the connection between the indi­vidual parts of the overall system becomes more and more signi­ficant. In this case, the system can be described with a quantum field theory. 

“The experiment is very challenging,” says Jörg Schmied­mayer. “We need complete information about our quantum system, as best as quantum physics allows. For this, we have developed a special tomo­graphy technique. We get the information we need by perturbing the atoms just a bit and then observing the resulting dynamics. It's like throwing a rock into a pond and then getting information about the state of the liquid and the pond from the consequent waves.”

As long as the system's temperature does not reach absolute zero, this shared infor­mation has a limited range. In quantum physics, this is related to the coherence length - it indicates the distance to which particles quantumly behave similar, and thereby know from each other. “This also explains why shared information doesn't matter in a classical gas,” says Mohamma­damin Tajik. “In a classical many-body system, coherence disappears; you can say the particles no longer know anything about their neighboring particles.” The effect of tempera­ture and coherence length on mutual information was also confirmed in the experiment. (Source: TU Wien)

Reference: M. Tajik et al.: Verification of the area law of mutual information in a quantum field simulator, Nat. Phys., online 24. April 2023; DOI: 10.1038/s41567-023-02027-1

Link: Atom-Institute, Vienna Center for Quantum Science and Technology (J. Schmiedmayer), Technical University Vienna , Vienna, Austria