Hi all,
tomorrow we have a guest, Sania Jevtic from Imperial College, who will
tell us about recent results on steering. See below for title and
abstract. Note the special time; this is also due to the fact that she
is only in town tomorrow.
Subsequent meetings will be on a different day, and thanks to everyone
for filling out the doodle. It looks like Thursday afternoon is
perhaps the best option (also Wednesday afternoon, but then there's
also the physics colloquium, or Thursday morning, but it's morning. ;)
We should make a decision tomorrow.
Best,
-joe
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Title:
Quantum steering with positive operator valued measures
Abstract:
Quantum steering is one of the three forms of quantum non-locality,
the other two being Bell-nonlocality and entanglement. The quantum
steering scenario most closely resembles the seminal thought
experiment of Einstein, Podolsky, and Rosen (1935). Two distant
observers, Alice and Bob, each possess a quantum particle, and these
two particles are entangled. Alice can perform measurements on her
particle which affect, or “steer”, the state of Bob’s particle. The
fascinating aspect of this is that, for certain entangled states of
the two particles, Bob’s steered ensembles cannot be described in a
classical way, that is, using a model of local hidden states. Such
entangled states are called “steerable” (otherwise they are
unsteerable). Steerable states have been verified experimentally and
have proven advantageous in a variety of quantum information tasks.
Nevertheless, the set of steerable states is still very poorly
understood. Methods for checking whether a state is steerable have
been presented in cases when Alice’s measurements are restricted, for
example, she can only perform projective, measurements. There are
currently no known efficient methods for tackling steerability when
she has the ability to perform generalised measurements, known as
“positive-operator valued measures” (POVMs). By viewing the steering
as a problem of nested convex objects, we derive an inequality which
can help to determine the boundary of steerable vs unsteerable quantum
states for all measurements. Given an ansatz u for the "ensemble of
local hidden states", we can systematically test whether a given
entangled state is unsteerable with respect to u. We test our
inequality on a “Werner state” and confirm (numerically to a high
precision) a longstanding conjecture that Werner state is unsteerable
for all measurements when it is an equal mixture of the maximally
mixed state and a singlet. As a novel application, we also test our
inequality on states that are mixtures of Bell pairs (“T-states”), and
our numerics indicate that here also steerability for all measurements
coincides with steerability for projective measurements.