Friday, October 6, 2017 3:30 pm
-
3:30 pm
EDT (GMT -04:00)
Ping Zhong, Department of Pure Mathematics, University of Waterloo
"Estimates for compression norms and additivity violation in quantum information"
The
free
compression
norm
(or
the
(t)-norm)
was
introduced
by
Belinschi,
Collins
and
Nechita
as
a
tool
to
compute
the
typical
location
of
the
collection
of
singular
values
associated
to
a
random
subspace
of
the
tensor
product
of
two
Hilbert
spaces.
In
turn,
it
was
used
by
them
to
obtain
the
limit
of
minimum
output
entropy
of
random
quantum
channels
in
the
appropriate
asymptotic
regime.
They
also
obtained
sharp
bounds
for
the
violation
of
the
additivity
of
the
minimum
output
entropy
for
random
quantum
channels
with
Bell
state
as
input
state
for
the
product
of
random
quantum
channels
with
the
conjugate
channels.
In
this
talk,
I
will
discuss
some
free
probability
techniques
involved
in
the
study
of
(t)-norm
and
their
applications
to
the
additivity
violations.
In
particular,
I
will
discuss
an
estimation
of
(t)-norm
and
a
conceptual
proof
of
the
additivity
violations. The
talk
is
based
on
joint
work
with
B.
Collins
and
M.
Fukuda.
MC
5417