William Slofstra, Institute for Quantum Computing, University of Waterloo
"Tsirelson's problem and linear system games"
In
quantum
mechanics,
physical
systems
are
modeled
by
Hilbert
spaces.
For
physical
systems
consisting
of
two
separated
subsystems,
a
standard
axiom
states
that
the
Hilbert
space
should
be
the
tensor
product
of
the
Hilbert
spaces
for
the
subsystems.
However,
there
is
another
less
restrictive
way
to
model
such
systems:
require
only
that
the
algebras
of
observables
commute
with
each
other.
Tsirelson's
problem
(of
which
there
are
several
variants)
asks
whether
the
quantum
correlations
coming
from
commuting-operator
models
can
always
be
realized
using
tensor-product
models.
The
most
important
of
these
problems,
the
"weak"
Tsirelsonproblem,
is
known
to
be
equivalent
to
a
famous
open
problem
in
operator
algebras,
the
Connes
embedding
problem.
While
we're
likely
still
very
far
from
being
able
to
resolve
the
weak
Tsirelson
problem,
I
will
explain
how
we
can
resolve
another
version
of
this
problem,
the
"middle"
Tsirelsonproblem,
by
using
something
called
linear
system
games
to
reduce
to
a
problem
in
group
theory.
MC 5501
Refreshments will be served in MC 5403 at 3:30 p.m. Everyone is welcome to attend.