Applications and the Future - Codes: The Guide to Secrecy from Ancient to Modern Times - page 365

9.5 Quantum Cryptography
The lesson to be extracted from the latest century of physics is that physical
knowledge has greatly expanded and resulted in new and much-improved theories,
but that these have been produced largely cumulatively and without a complete
break with the past.
Helge Kragh (1944-)
— from Quantum Generations (see [140, page 449])
The nobel laureate, Richard Feynman, 9.31 once said: “ I think that it is safe
to say that nobody understands quantum mechanics .” The science of Quan-
tum 9.32 mechanics is the branch of physics that accounts for matter at the
atomic level. We will not try to explain quantum mechanics beyond this ele-
mentary description. However, a cornerstone of quantum cryptography, called
the uncertainty principle , 9.33 may be relatively easily stated as: One cannot
simultaneously know both the position and momentum of a given object to ar-
bitrary precision. 9.34 This is usually illustrated as follows. Suppose that we
wish to measure the position and momentum of a specific particle. To do this,
we must “see” the particle so we must shine light on it. Suppose that light has
wavelength λ . To measure the particle's position, λ must be very short, because
in order to provide data on position we need wavelengths comparable to the
object we want to locate. However, a short wavelength of light transmits a big
boost in momentum when it bounces off the particle to provide position data.
Thus, the more accurately we measure position, the more uncertainty there is
in its momentum. On the other hand, if we want to measure momentum, we
use very longwavelenths, which increases uncertainty in its position. Hence,
a particle does not have a well-defined simultaneous position and momentum.
Typically, quantum experiments are done at this subatomic particle level, and
this is not in our everyday experience. Yet, there is a means of describinga
quantum experiment at a level with which we are all familiar.
9.31 Richard Phillips Feynman (1918-1988) was born in New YorkCity on May 11, 1918. He
was educated in the United States, obtaining a doctorate from Princeton in 1942, wherein his
thesis developed a new approach to quantum mechanics. From 1943 to 1945, he worked as a
member of the team that developed the first atomic bomb at Los Alamos. In 1965, he was
awarded the Nobel Prize in Physics. Despite all his accomplishments, he was not a typical
stuffy scientist. To put his life in perspective, we quote from the jacket cover of his topic [86]:
“In short, here is Feynman's life in all its eccentric glory — a combustible mixture of high
intelligence, unlimited curiosity, and raging chutzpah.” After eight years of battling abdominal
cancer, he succumbed on February 15, 1988, in Los Angeles, at the age of sixty-nine, having
taught his students up until two weeks before his death.
9.32 Quantum theory is a physical theory that holds that certain properties occur only in
discrete (as opposed to continuous) amounts, called quanta .
9.33 This is formally known as Heisenberg's uncertainty principle , named after Werner Karl
Heisenberg (1901-1976) who was awarded the Nobel Prize for Physics in 1932.
9.34 This does not say anything about how precisely a particular object can be known. It does
say (more generally), that some pairs of properties are intimately linked in such a way that
they cannot be precisely measured at the same time. Physicists call these pairs canonically
conjugate variables . For instance, position and momentum is one such pair and another is
time and energy. The more precisely one knows the time span when an event occurred, the
less precisely one knows the energy involved (and vice versa).