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Quantum Steering
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Quantum correlations between two parties are essential for the argument of Einstein, Podolsky, and Rosen in favour of the incompleteness of quantum mechanics. Schr\"odinger noted that an essential point is the fact that one party can influence the wave function of the other party by performing suitable measurements. He called this phenomenon quantum steering and studied its properties, but only in the last years this kind of quantum correlation attracted significant interest in quantum information theory. In this paper the theory of quantum steering is reviewed. First, the basic concepts of steering and local hidden state models are presented and their relation to entanglement and Bell nonlocality is explained. Then various criteria for characterizing steerability and structural results on the phenomenon are described. A detailed discussion is given on the connections between steering and incompatibility of quantum measurements. Finally, applications of steering in quantum information processing and further related topics are reviewed.
Forward citations
Cited by 5 Pith papers
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Measurement incompatibility and quantum steering via linear programming
A hierarchy of linear programs computes provable upper and lower bounds on measurement incompatibility and quantum steering, scaling polynomially with the number of measurements.
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The complexity of compatible measurements
For any set of m compatible quantum measurements, a parent measurement exists with at most d^2(m(o-1)+1) non-vanishing outcomes, a bound linear in the number of measurements, with small cases where the maximal complex...
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The Complementary Information Principle of Quantum Mechanics
The paper derives tight, SDP-computable majorization bounds for the probability vector of a post-test measurement conditioned on a pre-test outcome, and uses them to outer-approximate arbitrary uncertainty regions.
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Quantum steering in a qubit-field system
For a qubit coupled to a single-mode field, heterodyne detection on the field steers the qubit over the full Bloch sphere for the pure entangled states studied, and can produce non-ellipsoidal steering sets for mixed states.
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Geometry on the manifold of Gaussian quantum channels
Analytical relative volumes of entanglement-breaking and incompatibility-breaking one-mode Gaussian channels are derived from a Hilbert-Schmidt geometry induced by the Choi-Jamiolkowski isomorphism.
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