Entanglement is a property in quantum mechanics that seemed so unbelievable and so lacking in detail that, 66 years ago this spring, Einstein called it “spooky action at a distance.” But a mathematician at Case Western Reserve University and two of his recent PhD graduates show entanglement is actually prevalent in large quantum systems and have identified the threshold at which it occurs.

The finding holds promise for the ongoing push to understand and take advantage of the property. If harnessed, entanglement could yield super high-speed communications, hack-proof encryptions and quantum computers so fast and powerful they would make today’s supercomputers look like adding machines in comparison.

The mathematicians don’t tell us how entanglement works, but were able to put parameters on the property by combining math concepts developed for a number of different applications during the last five decades. In a nutshell, the researchers connected the math to properties of quantum mechanics—the otherworldly rules that best apply to atomic and subatomic particles—to describe physical reality.

“There have been indications that large subgroups within quantum systems are entangled,” said Stanislaw Szarek, mathematics professor at Case Western Reserve and an author of the study. “Our contribution is to find out exactly when entanglement becomes ubiquitous.”

Szarek worked with Guillaume Aubrun, assistant professor of mathematics at Université Claude Bernard Lyon 1, France, and Deping Ye, assistant professor of mathematics and statistics at Memorial University of Newfoundland, Canada. Their work is published online in the Early View section of *Communications on Pure and Applied Mathematics*.

The behaviors of materials down at the level of atoms are often strange, but entanglement borders on our concepts of sorcery. For example, if two electrons spinning in opposite directions are entangled, when one changes direction, the other immediately changes, whether the electrons are side by side, across the room or at opposite ends of the universe.

Read more at: Phys.org