68,293 research outputs found
The Quantum Frontier
The success of the abstract model of computation, in terms of bits, logical
operations, programming language constructs, and the like, makes it easy to
forget that computation is a physical process. Our cherished notions of
computation and information are grounded in classical mechanics, but the
physics underlying our world is quantum. In the early 80s researchers began to
ask how computation would change if we adopted a quantum mechanical, instead of
a classical mechanical, view of computation. Slowly, a new picture of
computation arose, one that gave rise to a variety of faster algorithms, novel
cryptographic mechanisms, and alternative methods of communication. Small
quantum information processing devices have been built, and efforts are
underway to build larger ones. Even apart from the existence of these devices,
the quantum view on information processing has provided significant insight
into the nature of computation and information, and a deeper understanding of
the physics of our universe and its connections with computation.
We start by describing aspects of quantum mechanics that are at the heart of
a quantum view of information processing. We give our own idiosyncratic view of
a number of these topics in the hopes of correcting common misconceptions and
highlighting aspects that are often overlooked. A number of the phenomena
described were initially viewed as oddities of quantum mechanics. It was
quantum information processing, first quantum cryptography and then, more
dramatically, quantum computing, that turned the tables and showed that these
oddities could be put to practical effect. It is these application we describe
next. We conclude with a section describing some of the many questions left for
future work, especially the mysteries surrounding where the power of quantum
information ultimately comes from.Comment: Invited book chapter for Computation for Humanity - Information
Technology to Advance Society to be published by CRC Press. Concepts
clarified and style made more uniform in version 2. Many thanks to the
referees for their suggestions for improvement
Information Causality, the Tsirelson Bound, and the 'Being-Thus' of Things
The principle of `information causality' can be used to derive an upper
bound---known as the `Tsirelson bound'---on the strength of quantum mechanical
correlations, and has been conjectured to be a foundational principle of
nature. To date, however, it has not been sufficiently motivated to play such a
foundational role. The motivations that have so far been given are, as I argue,
either unsatisfactorily vague or appeal to little if anything more than
intuition. Thus in this paper I consider whether some way might be found to
successfully motivate the principle. And I propose that a compelling way of so
doing is to understand it as a generalisation of Einstein's principle of the
mutually independent existence---the `being-thus'---of spatially distant
things. In particular I first describe an argument, due to Demopoulos, to the
effect that the so-called `no-signalling' condition can be viewed as a
generalisation of Einstein's principle that is appropriate for an irreducibly
statistical theory such as quantum mechanics. I then argue that a compelling
way to motivate information causality is to in turn consider it as a further
generalisation of the Einsteinian principle that is appropriate for a theory of
communication. I describe, however, some important conceptual obstacles that
must yet be overcome if the project of establishing information causality as a
foundational principle of nature is to succeed.Comment: '*' footnote added to page 1; 24 pages, 1 figure; Forthcoming in
Studies in History and Philosophy of Modern Physic
The Role of Relative Entropy in Quantum Information Theory
Quantum mechanics and information theory are among the most important
scientific discoveries of the last century. Although these two areas initially
developed separately it has emerged that they are in fact intimately related.
In this review I will show how quantum information theory extends traditional
information theory by exploring the limits imposed by quantum, rather than
classical mechanics on information storage and transmission. The derivation of
many key results uniquely differentiates this review from the "usual"
presentation in that they are shown to follow logically from one crucial
property of relative entropy. Within the review optimal bounds on the speed-up
that quantum computers can achieve over their classical counter-parts are
outlined using information theoretic arguments. In addition important
implications of quantum information theory to thermodynamics and quantum
measurement are intermittently discussed. A number of simple examples and
derivations including quantum super-dense coding, quantum teleportation,
Deutsch's and Grover's algorithms are also included.Comment: 40 pages, 11 figure
A quantum-information-theoretic complement to a general-relativistic implementation of a beyond-Turing computer
There exists a growing literature on the so-called physical Church-Turing
thesis in a relativistic spacetime setting. The physical Church-Turing thesis
is the conjecture that no computing device that is physically realizable (even
in principle) can exceed the computational barriers of a Turing machine. By
suggesting a concrete implementation of a beyond-Turing computer in a spacetime
setting, Istv\'an N\'emeti and Gyula D\'avid (2006) have shown how an
appreciation of the physical Church-Turing thesis necessitates the confluence
of mathematical, computational, physical, and indeed cosmological ideas. In
this essay, I will honour Istv\'an's seventieth birthday, as well as his
longstanding interest in, and his seminal contributions to, this field going
back to as early as 1987 by modestly proposing how the concrete implementation
in N\'emeti and D\'avid (2006) might be complemented by a
quantum-information-theoretic communication protocol between the computing
device and the logician who sets the beyond-Turing computer a task such as
determining the consistency of Zermelo-Fraenkel set theory. This suggests that
even the foundations of quantum theory and, ultimately, quantum gravity may
play an important role in determining the validity of the physical
Church-Turing thesis.Comment: 27 pages, 5 figures. Forthcoming in Synthese. Matches published
versio
Transmitting a signal by amplitude modulation in a chaotic network
We discuss the ability of a network with non linear relays and chaotic
dynamics to transmit signals, on the basis of a linear response theory
developed by Ruelle \cite{Ruelle} for dissipative systems. We show in
particular how the dynamics interfere with the graph topology to produce an
effective transmission network, whose topology depends on the signal, and
cannot be directly read on the ``wired'' network. This leads one to reconsider
notions such as ``hubs''. Then, we show examples where, with a suitable choice
of the carrier frequency (resonance), one can transmit a signal from a node to
another one by amplitude modulation, \textit{in spite of chaos}. Also, we give
an example where a signal, transmitted to any node via different paths, can
only be recovered by a couple of \textit{specific} nodes. This opens the
possibility for encoding data in a way such that the recovery of the signal
requires the knowledge of the carrier frequency \textit{and} can be performed
only at some specific node.Comment: 19 pages, 13 figures, submitted (03-03-2005
- …