Exact Formula Derived for Entanglement Distillation in Quantum Systems

[frankerkanol]

A mathematical physicist from RIKEN, in collaboration with a researcher from the University of Amsterdam, has derived an exact expression for a fundamental process critical to many quantum technologies. This breakthrough could provide important theoretical guidance for the future development of quantum computing, communication, and other entanglement-based technologies.

Quantum technologies often rely on the phenomenon of entanglement, where particles remain deeply connected regardless of the distance between them, displaying correlations that surpass what is possible in classical systems. However, creating the pure, noise-free entangled states that these technologies require is extremely difficult in practice, as most real-world systems produce noisy and weakly entangled states due to technological imperfections.

To address this issue, scientists use a process known as entanglement distillation, or purification, which extracts a smaller number of high-quality entangled states from a larger set of imperfect ones. Despite its importance, calculating the rate at which this distillation can occur has remained an open challenge in most general scenarios.

“Entanglement distillation is essential because there is this gap between the pure entanglement that quantum protocols require and the noisy entanglement we can prepare in the lab,” explained Bartosz Regula of the RIKEN Center for Quantum Computing.

Together with Ludovico Lami of the University of Amsterdam, Regula has now derived an exact expression for the distillation rate under less restrictive conditions. This is only the second time such an expression has been obtained in the field. Their findings, published in Nature Communications, resolve a theoretical problem that has lingered for nearly two decades.

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In the early 2000s, a series of studies proposed connections between entanglement distillation and a concept known as relative entropy. However, those conclusions were recently revisited after flaws were discovered in the original mathematical proofs. The new work successfully clarifies and corrects that line of inquiry.

Regula noted that they had anticipated a possible relationship, but the exact result came as a pleasant surprise. “We suspected that there might be a relationship,” he said. “But it was a nice surprise when we were able to find an exact expression for it.”

The new formula applies to scenarios involving a large number of quantum states, which makes it primarily theoretical for now. Experimental systems are still far from being able to manipulate the vast number of quantum bits required to observe the predicted rates.

“This is a case where theory is far ahead of experiments,” said Regula. “To see these rates, we’d need to manipulate many, many quantum systems at the same time, but experimentalists currently struggle to manipulate even tens or hundreds of quantum bits.”

[FrankJScott]

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