Quantum
Information Science (QIS) Seminar
(CSI 991 - 006)
Monday,
George Mason University,
Science Showcase,
Presenter: Jeff
Tollaksen, Assistant Professor,
Title: Time-symmetric
Quantum Mechanics and Implications for
Quantum Information
Abstract: In this
talk, I will review a Gedanken-experiment in which, following one line
of
reasoning, an electron is said to be definitely in one location. On the
other
hand, following an alternative reasoning, the same electron is said to
be
definitely in another location.
As with many well-known quantum paradoxes, the paradoxical effects
appear only
when one discusses results of experiments which do not actually take
place.
That is, when the experiments do take place, they disturb the system in
such a
way that the paradoxical effects disappear. Hence the paradox is
usually
dismissed as non-physical. Rather than dismissing the paradox, I argue
that
when a new set of measurements developed by our group is applied to the
paradox, then strange and surprising experimental outcomes are
obtained. E.g.,
our theory predicts that an actual measurement will indicate a negative
number
of particles. Actual experiments were subsequently performed and their
results
were in very good agreement with our theoretical predictions.
These paradoxes point to a deeper structure inherent to quantum
mechanics which
obeys a simple, intuitive, and self-consistent logic. (see
Aharonov...Tollaksen, Phys. Lett. A, 301, p. 130-, 2002; and New
Scientist
cover story "They said it couldn't be done, but now we can see inside
the
quantum world," May 2003).
To describe these deeper structures, we have developed novel
descriptions which
characterize quantum systems during the time interval between two
successive
ideal measurements, described theoretically by weak values and
experimentally
by weak measurements. Ideal measurements are precise but disturb the
system.
Weak measurements limit disturbance and are constructed from a new kind
of
ensemble: the pre-and-post-selected ensemble. In the usual
(pre-selected-only)
ensemble, a system is prepared and measurements are performed. In pre-
and
post-selected ensembles, we add another final measurement, which
divides the
pre-selected-only ensemble into sub-ensembles characterized by the
initial and
final measurement outcomes. Post-selection reflects unique aspects of
quantum
mechanics: measurement results are not determined by equations of
motion and
initial conditions. Weak value distributions of pre-and-post-selected
ensembles
are dramatically different from eigenvalue distributions of
pre-selected-only
ensembles, and new information can be obtained about the system.
In addition, I will discuss the relevance of these discoveries to
quantum
information, including: 1) a new formulation of dynamics with
implications for
superdense coding, 2) implications for tunneling, computational
speed-up, and
cryptography, 3) optical applications, and 4) relevance to decoherence
and
temporal control of correlations.
About
the Author: Assistant
Professor, School of Computational Sciences, Ph.D.,