Jaarboek no. 89. 2010/2011 - Koninklijke Maatschappij voor ...

Natuurkundige voordrachten I Nieuwe reeks 89
Quantum Information, Nonlocal Games and Quantum Cryptography
Dr. S. Fehr
Centrum voor Wiskunde en Informatica, Amsterdam
Introduction
The story of quantum mechanics begins at the turn
of the twentieth century, when a series of crises had
arisen in physics. The problem was that the theories
of physics at that time (now called classical physics)
were predicting absurdities, like an ΄ultraviolet
catastrophe΄ involving infinite energies, or electrons
spiraling inescapably into the atomic nucleus.
At first, these problems were resolved by means of
additional ad hoc hypotheses; however, over time
and with an increased understanding of atoms and
radiation, these attempted explanations became
more and more obscure. The crisis came to a head
in the early 1920’s, after a quarter century of turmoil,
and resulted in the creation of the theory of quantum
mechanics. The rules of quantum mechanics are
simple but even experts find them counter intuitive.
΄Anyone who is not shocked by quantum theory has
not understood a single word΄ is a famous quote
by Niels Bohr. Inherent to quantum mechanics are
strange effects that appear to contradict our daily
experiences with Nature. We briefly mention the following
two. The superposition principle states that if
a quantum system may be in two (or more) possible
states, then it may also be in a superposition of the
two. For example, if a particle can travel through
two possible slits, then its path may actually be a
superposition of passing through one or the other
slit. Heisenberg’s uncertainty relation states that it
is impossible to have full knowledge about certain
pairs of physical properties of a quantum system,
like to have full knowledge of the position and the
momentum of a particle. As a matter of fact, according
to quantum mechanics, the situation is even
stranger: not only can certain properties not be fully
known simultaneously, these properties are not even
determined up to the point in time where they are
measured, and the sole act of measuring one prop-
erty strongly affects other properties. Albert Einstein,
one of the best known critics of quantum mechanics,
expressed his discomfort with this situation by saying
΄I cannot believe that the moon exists only because a
mouse looks at it΄.
Figure 1
Werner Heisenberg.
The goal of looking at quantum mechanics from an
information-theoretic point of view is two-fold. First,
it sharpens our intuition about quantum mechanics
and makes the predictions of quantum mechanics
more transparent to human minds. For instance, the
theory of nonlocal games (as we discuss later) provides
a foundation for easy-to-understand experiments
for which classical and quantum physics give
different predictions (and for which so-far conducted
experiments contradict the predictions of classical
physics but are consistent with those of quantum
mechanics). And, second, quantum information
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