Some things are related, some are not. Suppose you randomly select one person from a crowd that is significantly taller than average. In that case, it is very likely that they also weigh more than 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 a large quantum system can “share” a certain amount of information. There are curious theoretical predictions about it: surprisingly, the extent of this “mutual information” does not depend on the size of the system but only on its surface. This surprising result has been experimentally confirmed at the Technical University of Vienna and published in physics of nature. 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.
Quantum information: more strongly connected than classical physics allows
“Let’s imagine a container of gas in which small particles fly and behave in a very classical way like small spheres,” says Mohammadamin Tajik from the Vienna Center for Quantum Science and Technology (VCQ) – TU Wien Atominstitut, first author of the current post. “If the system is in equilibrium, then the particles in different areas of the container do not know anything about each other. One can consider them completely independent of each other. Therefore, one can say that the mutual information that these two particles share is zero.”
In the quantum world, however, things are different: if the particles behave quantum, 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 quantum many-body system,” explains Mohammadamin Tajik. “In such a quantum gas, the shared mutual information is greater than zero, and it does not depend on the size of the subsystems, but 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 cover. In the quantum world, however, information is often closely related to surface area.
Measurements with ultracold atoms
An international research team led by Prof. Jörg Schmiedmayer has now confirmed for the first time that mutual information in a quantum many-body system scales with surface area rather than volume. To do this, they studied a cloud of ultracold atoms. The particles were cooled to just above absolute zero and held in place by an atomic chip. At extremely low temperatures, the quantum properties of particles become increasingly important. Information is spread 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, to the best of what quantum physics allows. For this, we have developed a special tomography technique. We get the information we need by perturbing the atoms a bit and then looking at the resulting dynamics. It’s like throwing a stone to a pond and then obtain information about the state of the liquid and the pond from the consequent waves”.
As long as the system temperature does not reach absolute zero (which is impossible), this “information sharing” is limited in scope. In quantum physics, this is related to the “coherence length”: it indicates the distance at which particles behave quantum similarly and thus know each other. “This also explains why the shared information does not matter in a classical gas,” says Mohammadamin Tajik. “In a classical many-body system, coherence disappears; one can say that 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.
Quantum information plays an essential role in many technical applications of quantum physics today. Therefore, the results of the experiment are relevant to several research areas, from solid state physics to the quantum physics study of gravity.
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