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I have a big dog in this fight, so all standard disclaimers apply. 

This is exciting news. The paper was just now published by Physical Review Letters, which is, of course, a flagship among physics journals. Here's an excerpt from the article in Gizmodo.

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"Most physicists believe that there is a richer and deeper theory of nature beyond quantum theory."

Quantum mechanics is the theory explaining the behavior of the smallest units of nature, like photons and electrons. Particles behave like waves (and vice versa), and before observing them, scientists can only explain the particles’ properties using probabilities. Rather than saying “this ball is blue,” they can only say “here are the chances this ball is blue or green.” But when two of these balls interact, they can become entangled, meaning you must describe both the balls’ properties at the same time. Measuring one of the balls’ colors directly implies what the color of the other ball will be, no matter how far away the balls are.

Scientists can observe entanglement. Chinese scientists set up this special inter-particle connection between light particles on a ground station and a satellite 100 kilometers away, for example. They observed correlations between the light particles in space and on Earth that couldn’t exist based on the laws of classical physics alone. Einstein hated entanglement since it implies that somehow, photons are influencing each other instantly without actually being near each other.

Richens’ team’s new paper, published yesterday in Physical Review Letters, doesn’t observe entanglement. Instead, “the main contribution of this work is to provide a compelling argument that entanglement—one of the most interesting and counterintuitive aspects of quantum theory—is an inescapable feature of any physical theory more “fundamental” than classical physics,”