Jaeger G. Quantum Information: An Overview
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Quantum Information
Gregg Jaeger
Quantum Information
An Overview
Dr. Gregg Jaeger
Quantum Imaging Laboratory
Department of Electrical and Computer Engineering
Boston University
8 Saint Mary’s Street
Boston, MA 02215
USA
and
Department of Natural Sciences
College of General Studies
871 Commonwealth Avenue
Boston, MA 02215
USA
jaeger@math.bu.edu
Library of Congress Control Number: 2006926441
ISBN-10: 0-387-35725-4 e-ISBN-10: 0-387-36944-9
ISBN-13: 978-0-387-35725-6 e-ISBN-13: 978-0-387-36944-0
Printed on acid-free paper.
C
2007 Springer Science+Business Media, LLC
All rights reserved. This work may not be translated or copied in whole or in part without the written
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To my daughter Alia and all those who have inspired, supported,
and/or prodded me
Foreword
In one word, this is a responsible book; the rest is commentary.
Around 1992 a few of us were led by Charles Bennett into a Garden of
Eden of quantum information, communication, and computation. No sooner
had we started exploring our surroundings and naming the birds and the
beasts, than Peter Shor put an end to that apparent innocence by showing
that factoring could be turned—by means of quantum hardware—into a poly-
nomial task. Fast factoring meant business; everybody seemed to be awfully
interested in factoring. Not that anyone had any use for factoring per se, but
it seemed that all the world’s secrets were protected by factor-keyed padlocks.
Think of all the power and the glory (and something else) that you might get
by acting as a consultant to big businesses and government agencies, helping
them pick everyone else’s locks and at the same time build unpickable ones
(well, nearly unpickable) for themselves. And if one can get an exponential
advantage in factoring, wouldn’t an exponential advantage be lying around
the corner for practically any other computational task? Quantum informa-
tion “and all that” has indeed blossomed in a few years into a wonderful new
chapter of physics, comparable in flavor and scope to thermodynamics. It has
also turned into a veritable “industry”—producing papers, conferences, exper-
iments, effects, devices—even proposals for quantum computer architectures.
Dutifully, also entire books on the subject have been appearing with a certain
regularity. Every time I see a new one, my first reaction tends to be, “Who
ordered that?” meaning, What needs does this book fill? What market does
it address?
I’m convinced that a bona fide academic book (as contrasted to a com-
mercial book) is first and foremost a knowledge-structuring exercise, a taut
“clothesline” (to use an image by Herbert Wilf) on which to neatly pin one’s
thoughts and find them still there in the morning. In this respect, the present
work is no exception. But one doesn’t have to go through all the labor of
producing a real book just for that. A second, also quite honorable motive, is
to let your colleagues know that you’ve been there yourself; that you’ve seen
a few things that they may have missed; that from a certain angle you get
viii Foreword
a much better view; and so on; that, in other words, by your meisterst¨uck
you claim full membership in the guild. In the meantime your colleagues had
of course been looking at what you were doing all along, and probably had
already made you member in pectore. I have no doubts that this applies to
the present case.
But in many, perhaps most, of the books I’ve seen I believe I detected in
an obstinate bass line, some sort of rumbling or blurbing that has no words
to it but I would be tempted to interpret like this: “Yes, this book of ours will
be good for an advanced undergraduate course in Quantum Computation,
Quantum Cryptography, or Entanglement Distillation (or any other permu-
tation of a number of similar sexy terms). But the real reason you must want
it, for yourself and for your students, is because we are nearing the moment
when a Quantium—rumored to be able to do all computations exponentially
faster—is to be commercially available as a drop-in replacement for the Pen-
tium! You need this book because you cannot afford not to be yourself one
of the very designers of the Quantium, or at least one of the first to design
it in!” I may just be hearing voices. But Quantum Information, Communica-
tion, and Computation is too rich a conceptual discipline to need debasing
with the subliminal lure of “universal exponential speedup.” For the moment
such a promise should be kept in the same class as “Energy so cheap it won’t
be worth metering;” it doesn’t even have to be false to be irresponsible. This
book steers clear of all that.
I recall the title of E.T. Jaynes’s book on information theory, Probability—
The Logic of Physics, and paraphrase it as “the logic of incomplete informa-
tion,” thus stressing that physics, even though central for motivation, is, from
a conceptual viewpoint, merely incidental to information theory. An incom-
plete description is just that, namely, one that is not sufficiently detailed to
identify a single individual: several individuals may fit it. The art of proba-
bility is nothing more than doing ordinary Aristotelian logic in parallel on all
those “several” (as often as not 10
24
) individuals, and in the end lumping the
results into “bins” according to whatever traits are relevant to our question
of the moment. Introducing (that is, making up) a probability distribution is
in essence equivalent to doing some of that binning before putting the system
through the “logic engine” rather than after. In fact, if this is done prop-
erly, the two approaches commute, and the second, of course, may save much
computational effort.
Quantum behavior has confronted physics with many novelties. What mat-
ters here is that it has introduced formerly unsuspected ways for a description
to be incomplete. Introduced where? into physics? My gut feeling is that in
this business physics per se is largely irrelevant. (Think, for example, of how
entropy, introduced for very good reasons by physicists, is in fact the funda-
mental quantitative parameter of any probability distribution—and thus, as
we’ve seen—an essential aspect of any incomplete description.) Be that as it
may, one of the duties of information theory is to acknowledge these new as-
pects of incompleteness whose prototype is found in physics and incorporate
Foreword ix
them by adding the necessary new modules to the underlying “logic engine”
mentioned above. There is no need to attempt to “interpret” or “explain”
quantum mechanics before setting about this task; on the contrary, having
in hand the resulting formal “quantum-enhanced” information theory may in
the end make it easier to address the interpretation problem itself.
Jaeger’s book seems to me consistent with the above strategy. That is, it
takes quantum mechanics as a premise. It doesn’t waste time arguing about,
or changing, the premise itself, and concentrates instead on developing an
inference engine capable of handling premises of that kind. That’s how we get
Quantum Information Theory: An Overview rather than one more book on
“Quantum information communication computation and all that.”
Tommaso Toffoli