Monday, July 16, 2018 12:00 pm
-
12:00 pm
EDT (GMT -04:00)
Jitendra Prakash, Pure Mathematics, University of Waterloo
"Tsirelson's problems and entanglement breaking rank"
This
talk
will
have
two
parts.
In
the
first
part,
we
consider
a
bipartite
system
with
two
observers,
Alice
and
Bob,
who
are
performing
measurements
in
their
labs.
There
are
two
models
of
quantum
mechanics
which
describe
the
joint
lab
of
Alice
and
Bob
-
the
quantum
model
and
the
commuting
quantum
model.
Tsirelson's
original
question
asked
whether
these
two
models
were
essentially
the
same.
We
show
that
these
two
models
are
different
for
bipartite
systems
with
five
quantum
experiments
and
binary
outcomes
for
each
experiment,
by
using
the
notion
of
correlation
functions
of
graphs.
In
the
second
part,
we
introduce
the
notion
of
entanglement
breaking
rank
of
an
entanglement
breaking
map.
We
show
that
computing
the
entanglement
breaking
rank
of
the
entanglement
breaking
map
defined
by
$$X
\mapsto
\frac{1}{d+1}(X+\mathrm{Tr}(X)),$$
where
$X\in
M_d(\mathbb
C)$
is
equivalent
to
the
existence
problem
of
SIC
POVM
in
dimension
$d$.