Aspects of M-theory and quantum information
Author(s)
Borsten, Leron
Type
Thesis
Abstract
As the frontiers of physics steadily progress into the 21st century we should bear in mind that the
conceptual edifice of 20th-century physics has at its foundations two mutually incompatible theories;
quantum mechanics and Einstein’s general theory of relativity. While general relativity refuses to
succumb to quantum rule, black holes are raising quandaries that strike at the very heart of quantum
theory. M-theory is a compelling candidate theory of quantum gravity. Living in eleven dimensions
it encompasses and connects the five possible 10-dimensional superstring theories. However, Mtheory
is fundamentally non-perturbative and consequently remains largely mysterious, offering up
only disparate corners of its full structure. The physics of black holes has occupied centre stage in
uncovering its non-perturbative structure.
The dawn of the 21st-century has also played witness to the birth of the information age and
with it the world of quantum information science. At its heart lies the phenomenon of quantum
entanglement. Entanglement has applications in the emerging technologies of quantum computing
and quantum cryptography, and has been used to realize quantum teleportation experimentally. The
longest standing open problem in quantum information is the proper characterisation of multipartite
entanglement. It is of utmost importance from both a foundational and a technological perspective.
In 2006 the entropy formula for a particular 8-charge black hole appearing in M-theory was found
to be given by the ’hyperdeterminant’, a quantity introduced by the mathematician Cayley in 1845.
Remarkably, the hyperdeterminant also measures the degree of tripartite entanglement shared by
three qubits, the basic units of quantum information. It turned out that the different possible types of
three-qubit entanglement corresponded directly to the different possible subclasses of this particular
black hole. This initial observation provided a link relating various black holes and quantum information
systems. Since then, we have been examining this two-way dictionary between black holes
and qubits and have used our knowledge of M-theory to discover new things about multipartite entanglement
and quantum information theory and, vice-versa, to garner new insights into black holes
and M-theory. There is now a growing dictionary, which translates a variety of phenomena in one
language to those in the other.
Developing these fascinating relationships, exploiting them to better understand both M-theory
and quantum entanglement is the goal of this thesis. In particular, we adopt the elegant mathematics
of octonions, Jordan algebras and the Freudenthal triple system as our guiding framework. In the
course of this investigation we will see how these fascinating algebraic structures can be used to
quantify entanglement and define new black hole dualities.
conceptual edifice of 20th-century physics has at its foundations two mutually incompatible theories;
quantum mechanics and Einstein’s general theory of relativity. While general relativity refuses to
succumb to quantum rule, black holes are raising quandaries that strike at the very heart of quantum
theory. M-theory is a compelling candidate theory of quantum gravity. Living in eleven dimensions
it encompasses and connects the five possible 10-dimensional superstring theories. However, Mtheory
is fundamentally non-perturbative and consequently remains largely mysterious, offering up
only disparate corners of its full structure. The physics of black holes has occupied centre stage in
uncovering its non-perturbative structure.
The dawn of the 21st-century has also played witness to the birth of the information age and
with it the world of quantum information science. At its heart lies the phenomenon of quantum
entanglement. Entanglement has applications in the emerging technologies of quantum computing
and quantum cryptography, and has been used to realize quantum teleportation experimentally. The
longest standing open problem in quantum information is the proper characterisation of multipartite
entanglement. It is of utmost importance from both a foundational and a technological perspective.
In 2006 the entropy formula for a particular 8-charge black hole appearing in M-theory was found
to be given by the ’hyperdeterminant’, a quantity introduced by the mathematician Cayley in 1845.
Remarkably, the hyperdeterminant also measures the degree of tripartite entanglement shared by
three qubits, the basic units of quantum information. It turned out that the different possible types of
three-qubit entanglement corresponded directly to the different possible subclasses of this particular
black hole. This initial observation provided a link relating various black holes and quantum information
systems. Since then, we have been examining this two-way dictionary between black holes
and qubits and have used our knowledge of M-theory to discover new things about multipartite entanglement
and quantum information theory and, vice-versa, to garner new insights into black holes
and M-theory. There is now a growing dictionary, which translates a variety of phenomena in one
language to those in the other.
Developing these fascinating relationships, exploiting them to better understand both M-theory
and quantum entanglement is the goal of this thesis. In particular, we adopt the elegant mathematics
of octonions, Jordan algebras and the Freudenthal triple system as our guiding framework. In the
course of this investigation we will see how these fascinating algebraic structures can be used to
quantify entanglement and define new black hole dualities.
Date Issued
2010-09
Date Awarded
2010-10
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Duff, Michael
Creator
Borsten, Leron
Publisher Department
Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)