Einstein-Podolsky-Rosen steering

Short answer: EPR steering is a category of quantum correlation that sits between mere nonseparability and Bell nonlocality. A Physical Review A paper builds steering inequalities from entropic uncertainty relations, a 2014 preprint derives a fine-grained steering inequality tied to one-sided device-independent key distribution, and a 2019 preprint proposes and demonstrates a device-independent steering verification protocol. These are laboratory and theory results.

Where steering sits

A Physical Review A paper hosted at the University of Rochester describes Einstein-Podolsky-Rosen steering as a level of quantum correlation strong enough to demonstrate the EPR paradox but not strong enough to rule out all models of local hidden variables. It places steering between Bell nonlocality and mere nonseparability. The authors develop steering inequalities for any set of observables that share a nontrivial entropic uncertainty relation, and use those relating discrete observables to build symmetric steering inequalities based on mutual information.

They motivate this by noting that for tasks such as verifying security in quantum key distribution with as few assumptions as possible, demonstrating entanglement is not enough, and witnesses of stronger correlation are needed.

A fine-grained steering inequality

The 2014 arXiv preprint (1404.7050) derives a steering inequality from a fine-grained uncertainty relation. The authors report that it can experimentally detect all steerable two-qubit Werner states with only two measurement settings on each side, which they say improves on previously known inequalities. According to their inequality, pure entangled states are maximally steerable, and with a slight change of setting the violation can be expressed as a function of the CHSH violation. They also prove that the violation is, up to a constant factor, a lower bound on the key rate of a one-sided device-independent quantum key distribution protocol secure against individual attacks.

Device-independent verification

The 2019 arXiv preprint (1909.13432) notes that Bell inequality violation gives a device-independent test but typically needs high measurement efficiency to close the detection loophole and low transmission loss. The authors propose and experimentally demonstrate a device-independent protocol to certify entanglement based on steering. They say it uses a measurement-device-independent technique and self-testing, can verify all bipartite steerable states, and in a three-measurement-setting scenario tolerates inefficient measurements and imperfect self-testing. They report a four-photon experiment for verification beyond Bell nonlocal states.

Limits

The 2014 and 2019 works are arXiv preprints, and the key-rate statement is a bound for one-sided device-independent protocols against individual attacks only. The experiment is a small photonic demonstration. None of the three works reports a deployed communication system.

FAQ

How does steering differ from Bell nonlocality?

The Physical Review A paper describes steering as strong enough to demonstrate the EPR paradox but not strong enough to rule out all local hidden variable models.

Can steering be detected with few measurements?

The 2014 preprint reports that its inequality detects all steerable two-qubit Werner states with only two measurement settings on each side.

Can steering be verified without trusting the devices?

The 2019 preprint proposes and experimentally demonstrates a device-independent protocol for this, using a measurement-device-independent technique and self-testing, and reports a four-photon experiment.

How does steering relate to key distribution?

The 2014 preprint proves that the violation of its inequality is, up to a constant factor, a lower bound on the key rate of a one-sided device-independent protocol secure against individual attacks.

Are pure entangled states maximally steerable?

According to the inequality in the 2014 preprint, yes.