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},
  year={2017},
  volume={80}
}
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… 
Applications of EPR steering in quantum teleportation and NOON states
Einstein-Podolsky-Rosen (EPR) steering refers to the type of correlations described in the EPR paradox, where one observer seems to affect (”steer”) the state of other observer by using local
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TLDR
In a quantum steering task, the correlations of Alice and Bob's measurement outcomes are tested against a classical probability bound which can be only violated if the state shared between the parties is quantum steerable.
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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
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TLDR
Two types of quantum steering scenarios are introduced for a tripartite quantum system, named “one-sided device-independent steering" and “two-sidedDevice- independent steering", which contains two levels according to the separability of the local hidden states and the independence of theLocal hidden variables, respectively.
Generalized Steering Robustness of Bipartite Quantum States
TLDR
A way of quantifying quantum steering, which is called the generalized steering robustness (GSR), is introduced and some interesting properties are established, including that every maximally entangled state has the maximal GSR.
High-dimensional measurement-device-independent quantum steering and its application in randomness generation
In a measurement-device-independent or quantum-refereed protocol, a referee can verify whether two parties share entanglement or Einstein-Podolsky-Rosen (EPR) steering without the need to trust
Experimental Measurement-Device-Independent Quantum Steering and Randomness Generation Beyond Qubits.
TLDR
The trust-free experimental verification of higher dimensional quantum steering is reported via preparing a class of entangled photonic qutrits and 1.106±0.023 bits of private randomness per every photon pair are extracted from observed data, which surpasses the one-bit limit for projective measurements performed on qubit systems.
Exposure of subtle multipartite quantum nonlocality
TLDR
It is shown that a naively defined criterion for multipartite steering allows for a contradictory effect whereby local operations could create steering seemingly from scratch, and protocols are devised that are able to reveal, in seemingly unsteerable systems, not only steering, but also Bell nonlocality.
Operational characterization of quantumness of unsteerable bipartite states
Recently, the quantumness of local correlations arising from separable states in the context of a Bell scenario has been studied and linked with superlocality [Phys. Rev. A {\bf 95}, 032120 (2017)].
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.
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References

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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
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
EPR Steering inequalities with Communication Assistance
TLDR
The set of bipartite quantum states which admits a local hidden state model augmented with c bits of classical communication from an untrusted party (Alice) to a trusted party (Bob) is characterized and it is conjectured that a state-of-the-art quantum experiment would be able to falsify two bits of communication this way.
Quantification of Gaussian quantum steering.
TLDR
A computable measure of steering for arbitrary bipartite Gaussian states of continuous variable systems is introduced, which reduces to a form of coherent information, which is proven never to exceed entanglement, and to reduce to it on pure states.
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