Researchers have unveiled a groundbreaking conjecture that sheds light on the entanglement properties of arbitrary spacetime regions within three-dimensional conformal field theory (CFT). This conjecture, presented recently in Physical Review Letters, proposes a novel approach to understanding the constraints that entanglement imposes on Quantum Field Theories.
The study, coauthored by Pablo Bueno (Institute of Cosmos Sciences of the University of Barcelona - ICCUB), uses fundamental properties of quantum entanglement to identify new bounds on the space of physically allowed quantum field theories in three dimensions.
Conformal field theories (CFTs) describe quantum systems whose physical properties remain unchanged under scale transformations (transformations which preserve angles).
These theories are important because, as the energy scale of any given system is varied, very often it reaches a point in which it becomes describable in terms of a certain CFT, which can be very useful. As a consequence of this fact, CFTs have applications in areas as diverse as condensed matter, particle physics or quantum gravity.
Characterising the set of physically feasible CFTs (those CFTs compatible with the laws of physics) is then an important problem which has received much attention in recent years. In this letter, the authors propose a new universal bound on the amount of quantum entanglement shared by a given spacetime region and its complement valid for general CFTs in three spacetime dimensions.
What is Quantum Entanglement?
Entanglement is perhaps the most fundamental property of quantum systems. It explains how two subatomic particles can be intimately linked to each other even if separated by millions of light-years of space. In a precise sense, two electrons in an entangled state should be thought of as a single inseparable entity, rather than two. Entanglement has measurable consequences and, as it turns out, the Nobel Prize in Physics 2022 has been awarded to Alain Aspect, John F. Clauser and Anton Zeilinger for developing increasingly precise experiments which have established, beyond any reasonable doubt, that entanglement is a fundamental property of nature. While traditionally considered within the quantum information/computation areas, in recent years there has been a surge in interest on the role played by quantum entanglement in the Quantum Field Theory context, which is the state-of-the-art framework for describing nature at its most fundamental level. It provides an exceptionally precise unified description of all known types of matter and physical interactions (with the exception of gravity).
A new bound on the entanglement of quantum fields
In the article, the authors present compelling evidence that the degree of entanglement of quantum fields in a general spacetime region can never exceed the one corresponding to a free scalar field —the simplest possible CFT which does not interact with any other particles. An important consequence is that the free scalar gives rise to an upper bound for the ratio of two fundamental quantities which characterise any CFT: the coefficient which controls energy correlations between different spatial points, and the partition function of the theory, which encodes statistical information about the thermodynamics of the system, when this is considered on a three-sphere. These two quantities have been subject of intense study in countless previous papers, but no general connection between the two had ever been found. These results fit harmoniously with previous four-dimensional results and generalise them using a novel set of ideas based on structural properties of quantum entanglement.
This groundbreaking research illustrates how looking at quantum field theory through the lens of entanglement allows to reveal universal features and patterns which would go completely unnoticed using more traditional methods. In doing so, it substantially advances our general understanding of conformal field theories and opens the door to various entanglement-based explorations in general spacetime dimensions.
For more information about this study, please refer to the full paper titled “Conformal Bounds in Three Dimensions from Entanglement Entropy” published in Physical Review Letters.
For media inquiries or additional information, please contact:
Pablo Bueno Gómez
ICCUB researcher and author of the paper
Anna Argudo Boter
ICCUB Communication’s Officer