Quantum Information Theory and the Foundations of Quantum Mechanics [thesis] - C. Timpson, Angielskie techniczne

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Quantum Information Theory and
The Foundations of Quantum
Mechanics
Christopher Gordon Timpson
The Queen’s College
A thesis submitted for the degree of Doctor of Philosophy
at the University of Oxford
Trinity Term 2004
Quantum Information Theory and the Foundations of
Quantum Mechanics
Christopher Gordon Timpson, The Queen’s College
Oxford University, Trinity Term 2004
Abstract of Thesis Submitted for the Degree of Doctor of
Philosophy
This thesis is a contribution to the debate on the implications of quantum information
theory for the foundational problems of quantum mechanics.
In Part I an attempt is made to shed some light on the nature of information and
quantum information theory. It is emphasized that the everyday notion of information
is to be rmly distinguished from the technical notions arising in information theory;
however it is maintained that in both settings ‘information’ functions as an abstract
noun, hence does not refer to a particular or substance. The popular claim ‘Information
is Physical’ is assessed and it is argued that this proposition faces a destructive dilemma.
Accordingly, the slogan may not be understood as an ontological claim, but at best, as
a methodological one. A novel argument is provided against Dretske’s (1981) attempt
to base a semantic notion of information on ideas from information theory.
The function of various measures of information content for quantum systems is ex-
plored and the applicability of the Shannon information in the quantum context main-
tained against the challenge of Brukner and Zeilinger (2001). The phenomenon of quan-
tum teleportation is then explored as a case study serving to emphasize the value of
recognising the logical status of ‘information’ as an abstract noun: it is argued that the
conceptual puzzles often associated with this phenomenon result from the familiar error
of hypostatizing an abstract noun.
The approach of Deutsch and Hayden (2000) to the questions of locality and infor-
mation ow in entangled quantum systems is assessed. It is suggested that the approach
suers from an equivocation between a conservative and an ontological reading; and the
diering implications of each is examined. Some results are presented on the character-
ization of entanglement in the Deutsch-Hayden formalism.
Part I closes with a discussion of some philosophical aspects of quantum computation.
In particular, it is argued against Deutsch that the Church-Turing hypothesis is not
underwritten by a physical principle, the Turing Principle. Some general morals are
drawn concerning the nature of quantum information theory.
In Part II, attention turns to the question of the implications of quantum information
theory for our understanding of the meaning of the quantum formalism. Following some
preliminary remarks, two particular information-theoretic approaches to the foundations
of quantum mechanics are assessed in detail. It is argued that Zeilinger’s (1999) Founda-
tional Principle is unsuccessful as a foundational principle for quantum mechanics. The
information-theoretic characterization theorem of Clifton, Bub and Halvorson (2003)
is assessed more favourably, but the generality of the approach is questioned and it is
argued that the implications of the theorem for the traditional foundational problems
in quantum mechanics remains obscure.
Acknowledgements
It is my pleasant duty to thank a large number of people, and more than one institution,
for the various forms of help, encouragement and support that they have provided during
the time I have been working on this thesis.
The UK Arts and Humanities Research Board kindly supported my research with a
postgraduate studentship for the two years of my BPhil degree and a subsequent two
years of doctoral research. I should also like to thank the Provost and Fellows of The
Queen’s College, Oxford for the many years of support that the College has provided,
both material and otherwise. Reginae erunt nutrices tuae: no truer words might be
said. A number of libraries have gured strongly during the time I have been at Oxford:
I would like in particular to thank the sta at the Queen’s and Philosophy Faculty
libraries for their help over the years.
On a more personal note, I would like to extend my thanks and appreciation to
my supervisor Harvey Brown, whose good example over the years has helped shape my
approach to foundational questions in physics and who has taught me much of what I
know. I look forward to having the opportunity in the future to continue working with,
and learning from, him.
Another large debt of thanks is due to John Hyman, my earliest teacher in philosophy,
who has continued to oer a great deal of assistance and encouragement over the years;
and whose fearsome questioning helped show me what it is to do philosophy (and,
incidentally, alerted me to the dangers of pernicious theorising).
Jon Barrett and I started out on the quest to understand the foundations and phi-
losophy of physics at the same time, just about a decade ago, now. Since then, we have
shared much camaraderie and many conversations, several of which have found their
way into this thesis at one point or another. And Jon is still good enough to check my
reasoning and oer expert advice.
I would like to thank Jeremy Buttereld, Je Bub, Chris Fuchs and Antony Valentini,
all of whom have been greatly encouraging and who have oered useful comments on
and discussion of my work. In particular, I should single out Jos U
nk for his unstinting
help in sharing his expertise in quantum mechanics, uncertainty and probability; and for
providing me with a copy of his unpublished PhD dissertation on measures of uncertainty
and the uncertainty principle. My understanding of measures of information has been
heavily inuenced by Jos’s work.
The (rest of the) Oxford philosophy of physics mob are also due a great big thank-
you: one couldn’t hope for a more stimulating intellectual environment to work in. So
thanks especially to Katharine Brading, Guido Bacciagaluppi, Peter Morgan, Justin
Pniower, Oliver Pooley, Simon Saunders and David Wallace for much fun, support and
discussion (occasionally of the late-night variety).
A little further aeld, I would like to thank Marcus Appleby, Ari Duwell, Doreen
Fraser, Hans Halvorson, Michael Hall, Leah Henderson, Clare Hewitt-Horsman (in par-
ticular on the topic of Chapter 5), Richard Jozsa, James Ladyman, Owen Maroney,
Michael Seevink, Mauricio Suarez, Rob Spekkens and Alastair Rae, amongst others, for
stimulating conversations on information theory, quantum mechanics and physics.
Finally I should like to thank my parents, Mary and Chris Timpson, sine qua non,
bien sur; and my wife Jane for all her loving support, and her inordinate patience
during the somewhat extended temporal interval over which this thesis was nally run
to ground. (Oh, and she made most of the pictures too!)
Contents
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