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.