In a new study from Skoltech and the University of Kentucky, researchers
found a new connection between quantum information and quantum field theory.
This work attests to the growing role of quantum information theory across
various areas of physics. The paper was published in the journal Physical
Review Letters.

Quantum information plays an increasingly important role as an organizing
principle connecting various branches of physics. In particular, the theory
of quantum error correction, which describes how to protect and recover
information in quantum computers and other complex interacting systems, has
become one of the building blocks of the modern understanding of quantum
gravity.

“Normally, information stored in physical systems is localized. Say, a
computer file occupies a particular small area of the hard drive. By “error”
we mean any unforeseen or undesired interaction which scrambles information
over an extended area. In our example, pieces of the computer file would be
scattered over different areas of the hard drive. Error correcting codes are
mathematical protocols that allow collecting these pieces together to
recover the original information. They are in heavy use in data storage and
communication systems. Quantum error correcting codes play a similar role in
cases when the quantum nature of the physical system is important,” Anatoly
Dymarsky, Associate Professor at the Skoltech Center for Energy Science and
Technology (CEST), explains.

In a rather unexpected twist, scientists realized not too long ago that
quantum gravity – the theory describing quantum dynamics of space and time –
operates similar mathematical protocols to exchange information between
different parts of space. “The locality of information within quantum
gravity remains one of the few open fundamental problems in theoretical
physics. That is why the appearance of well-studied mathematical structures
such as quantum error correcting codes is intriguing,” Dymarsky notes. Yet
the role of codes was only understood schematically, and the explicit
mechanism behind the locality of information remains elusive.

In their new paper, he and his colleague, Alfred Shapere from the University
of Kentucky Department of Physics and Astronomy, establish a novel
connection between quantum error correcting codes and two-dimensional
conformal field theories. The latter describe interactions of quantum
particles and have become standard theoretical tools to describe many
different phenomena, from fundamental elementary particles to
quasi-particles emerging in quantum materials, such as graphene. Some of
these conformal field theories also describe quantum gravity via holographic
correspondence.

“Now we have a new playground to study the role of quantum error correcting
codes in the context of quantum field theory. We hope this is a first step
in understanding how locality of information actually works, and what hides
behind all this beautiful mathematics,” Dymarsky concludes.

## Reference:

Solutions of Modular Bootstrap Constraints from Quantum Codes by Anatoly
Dymarsky and Alfred Shapere, 21 April 2021, Physical Review Letters.
DOI: 10.1103/PhysRevLett.126.161602

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