Quantum steering: a review with focus on semidefinite programming.

@article{Cavalcanti2017QuantumSA,
  title={Quantum steering: a review with focus on semidefinite programming.},
  author={Daniel Cavalcanti and Paul Skrzypczyk},
  journal={Reports on progress in physics. Physical Society},
  year={2017},
  volume={80 2},
  pages={
          024001
        }
}
Quantum steering refers to the non-classical correlations that can be observed between the outcomes of measurements applied on half of an entangled state and the resulting post-measured states that are left with the other party. From an operational point of view, a steering test can be seen as an entanglement test where one of the parties performs uncharacterised measurements. Thus, quantum steering is a form of quantum inseparability that lies in between the well-known notions of Bell… 

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References

SHOWING 1-10 OF 232 REFERENCES
Steering Maps and Their Application to Dimension-Bounded Steering.
TLDR
The concept of steering maps is introduced, which allow us to unlock sophisticated techniques that were developed in regular entanglement detection and to use them for certifying steerability and enables a generalized dimension-bounded steering.
Steering bound entangled States: a counterexample to the stronger Peres conjecture.
TLDR
A method is provided to generate systematically bound entangled quantum states which can still be used for steering and, therefore, to rule out local hidden state models and sheds light on the relations between the various views on quantum correlations.
Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems.
TLDR
This work provides a hierarchy of sufficient conditions for the steerability of bipartite quantum states of any dimension, including continuous variable states, and provides a systematic framework to analytically derive nonlinear steering criteria.
Measures and applications of quantum correlations
TLDR
This work gives an overview of the current quest for a proper understanding and characterisation of the frontier between classical and quantum correlations (QCs) in composite states, and focuses on various approaches to define and quantify general QCs, based on different yet interlinked physical perspectives.
Natural Framework for Device-Independent Quantification of Quantum Steerability, Measurement Incompatibility, and Self-Testing.
TLDR
By proving a quantitative relationship between steering robustness and the recently introduced incompatibility robustness, this approach immediately provides a device-independent lower bound on the generalized robustness of entanglement, as well as the usefulness of the underlying quantum state for a type of subchannel discrimination problem.
All-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering
TLDR
This work presents a proof of steering without inequalities rendering the detection of correlations leading to a violation of steering inequalities unnecessary, and demonstrates that there exist many quantum states which do not violate any previously known steering inequality but are indeed steerable.
Entanglement verification and steering when Alice and Bob cannot be trusted
Various protocols exist by which a referee can be convinced that two observers share an entangled resource. Such protocols typically specify the types of communication allowed, and the degrees of
Necessary and sufficient quantum information characterization of Einstein-Podolsky-Rosen steering.
TLDR
It is proved that, for any bipartite steerable state, there are instances of the quantum subchannel discrimination problem for which this state allows a correct discrimination with strictly higher probability than in the absence of entanglement, even when measurements are restricted to local measurements aided by one-way communication.
Classical randomness in quantum measurements
Similarly to quantum states, also quantum measurements can be ‘mixed’, corresponding to a random choice within an ensemble of measuring apparatuses. Such mixing is equivalent to a sort of hidden
Measurement incompatibility and Schrödinger-Einstein-Podolsky-Rosen steering in a class of probabilistic theories
Steering is one of the most counter intuitive non-classical features of bipartite quantum system, first noticed by Schrodinger at the early days of quantum theory. On the other hand, measurement
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