Nicholas Manor, Department of Pure Mathematics, University of Waterloo
"Quantum Channels, Exactness, and Noncommutative Convexity"
This
presentation
will
consist
of
three
short
sections
discussing
separate
topics
of
my
PhD
research.
Section
one
will
discuss
joint
work
with
Matthew
Kennedy
and
Vern
Paulsen
about
the
connection
between
PPT
(positive
partial
transpose)
quantum
channels
and
their
connection
to
entanglement.
We
show
that
when
a
PPT
channel
is
composed
with
itself
repeatedly,
the
composition
becomes
entanglement
breaking
in
the
limit.
Section
two
will
discuss
exactness
for
locally
compact
groups
and
the
exactness
of
the
associated
reduced
C*-algebra.
We
show
that
for
a
broad
class
of
well
behaved
groups
these
two
properties
coincide.
Section
three
is
the
largest
and
will
discuss
two
projects
on
nc
(noncommutative)
convexity:
the
first
is
joint
work
with
Matthew
Kennedy
and
Se-Jin
Kim,
and
the
second
is
joint
work
with
Adam
Humeniuk
and
Matthew
Kennedy.
Davidson-Kennedy
showed
that
there
is
a
natural
duality
between
operator
systems
and
compact
nc
convex
sets,
and
we
extend
this
result
to
nonunital
operator
systems,
i.e.,
norm
closed
self-adjoint
subspaces
of
B(H).
More
recently,
C.K.
Ng
studied
the
duals
of
nonunital
operator
systems
and
asked
whether
these
duals
are
again
operator
systems.
They
answered
this
question
by
algebraically
characterizing
operator
systems
with
operator
system
duals.
We
expand
on
this
work
by
providing
a
characterization
in
terms
of
the
geometric
structure
of
the
compact
nc
convex
set
of
completely
contractive
and
completely
positive
maps
on
an
operator
system.
Online. Contact Nick Manor (nmanor@uwaterloo.ca) for more information.