Quantum discord and correlations beyond entanglement

Short answer: Quantum discord is a measure of quantum correlations that can be present in states that have no entanglement. A 2012 Reviews of Modern Physics review says that in many cases unentangled states show nonclassical behavior too, and that quantum correlations beyond entanglement indicate an advantage of quantum methods over classical ones in many cases. A 2017 review covers the same ground, plus multiparty discord and links to other areas. These are theory reviews, not hardware results.

Why look beyond entanglement

The 2012 review says one of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Entanglement is the most prominent of these, but in many cases unentangled states exhibit nonclassical behavior too. It concludes that distinguishing quantum correlations other than entanglement provides a better division between the quantum and classical worlds, especially for mixed states.

The 2017 review gives some history. It says that around 2001, analyses of different measures of information in quantum theory concluded that entanglement does not account for all non-classical correlations and that even separable states usually contain correlations that are not entirely classical. These correlations are named quantum discord. It adds that an intuitive argument was soon made that discord may be connected to the performance of certain quantum computers. It also cites the protocol of deterministic quantum computation with one quantum bit, discovered by Knill and Laflamme, as a case where the natural bipartite split of the system is unentangled even though the phenomenon is nonclassical, under a plausible assumption.

What the reviews cover

The 2012 review is in two halves. The first reviews the mathematical properties of the measures of quantum correlations, relates them to each other, and discusses the classical-quantum division common among them. The second shows that the measures identify and quantify deviation from classicality in quantum-information-processing tasks, quantum thermodynamics, open-system dynamics and many-body physics. The 2017 review describes quantum discord and related topics and their possible connections with quantum communication, quantum computation, many-body physics and open quantum dynamics, and also discusses discord in the multiparty regime.

Limits

These are review articles, so they report what the literature says rather than new experiments. The 2012 review says quantum correlations indicate an advantage "in many cases", which is not a general claim, and the computational connection in the 2017 review is described as an argument and a plausible-assumption result. Nothing here is a claim about a product.

FAQ

Can a state have discord without entanglement?

Yes, according to both reviews. The 2012 review says unentangled states often exhibit nonclassical behavior too.

What is the classical-quantum division?

A split of correlations into classical and quantum parts, which the 2012 review says is common among the measures it covers.

Is discord linked to quantum computing?

The 2017 review says an argument was made that discord may be connected to the performance of certain quantum computers, and cites deterministic quantum computation with one quantum bit as related.

Where else does it apply?

The 2012 review lists quantum thermodynamics, open-system dynamics and many-body physics.

Does it work for more than two parties?

The 2017 review discusses discord in the multiparty regime.