Physicists around the world are looking for theories that combine quantum physics and spacetime as described by Einstein. Now, researchers at the Austrian Academy of Sciences (ÖAW) have discovered an important connection between quantum correlation and quantum physics.
The essential principle between all physical interactions is locality. This states that any physical system can only interact with systems in their immediate environment. For remote systems, there must be an intermediate medium. A principle that can be understood, for instance, when telephoning with mobile phones, in which the data is transmitted via electromagnetic waves in order to be able to make contact with the person you are talking to.
Fourth dimension: Spacetime
Quantum physicists from the Austrian Academy of Sciences and the University of Vienna examined the principle of locality in terms of a connection between quantum mechanics and spacetime. Spacetime is the understanding of gravitation that stems from Albert Einstein’s general theory of relativity. That space which merges the three spatial dimensions with the fourth dimension of time (past, present, future).
Alice and Bob
The researchers worked on the correlation of two independently generated measurement results. At first, the fourth dimension was not taken into account: The starting point was three-dimensional space, in which two fictitious observers – Alice and Bob – explore two separate components of a physical system. Alice’s research area is limited (region of space) and Bob’s research area is outside of this limited space. Alice and Bob are synonyms for sender and recipient of a message. They are used to simplify explanations in physics.
Image above: Correlations generated by quantum entanglement are also referred to as quantum correlations. Measurement results on several entangled (interacting) subsystems are correlated, i.e. depending on the measurement results of one subsystem there is a modified probability distribution for the potential measurement results on the other subsystems.
Area law of entropy
The area law for the entanglement entropy is an essential law in quantum physics. It states that the correlation between the measurement results of Alice and Bob is proportional to the boundary area. But not to its volume, as one might easily assume when thinking in terms of three-dimensional space.
Building on the law of entropy, the scientists explored the scenario from the perspective of Time, the fourth dimension. Alice carries out her measurements in a circumscribed area of a space over a specified period of time. Bob measures outside of this range and has access to any other available points at any time. In this spacetime simulation, they wanted to find out what role the boundary between Alice and Bob means for the correlation between the measurement results.
They came to the conclusion that the area law of entropy also applies to spacetime. Provided the principle of locality is in force, this means the objects interact locally with each other. Also taking into account the dimension of time, the correlation of the measurement results from Alice and Bob is directly proportional to the area of the boundary area. Volume does not play a role in the extent of the correlation, not even in spacetime.
Časlav Brukner, team leader at the Institute for Quantum Optics and Quantum Information from the Austrian Academy of Sciences and one of the authors of the study, sees this finding as getting closer to a uniform theory for the worlds of quantum physics and gravitation. Quote: “We have succeeded in finding an important relationship between quantum correlation and spacetime.”
Publikation im Journal Quantum Information
Kull, I./ Allard Guérin, P./Brukner, Č. (2019): A Spacetime Area Law Bound on Quantum Correlations. Nature Partner Journal Quantum Information. (Open Access)