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Quantum entanglement—a connection between particles that produces correlations beyond what is classically possible—will be the backbone of future quantum technologies, including secure communication, cloud quantum computing, and distributed sensing. But entanglement is fragile; noise from the environment degrades entangled states over time, leaving scientists searching for methods to improve the fidelity of noisy entangled states.

Now, researchers at the University of Chicago Pritzker School of Molecular Engineering (UChicago PME), University of Illinois Urbana-Champaign, and Microsoft have shown that it is fundamentally impossible to design a single one-size-fits-all protocol to counteract that noise.

"In quantum information, we often hope for a protocol that works in all scenarios—a kind of cure-all," said Asst. Prof. Tian Zhong, senior author of the new work in ÃÈÃÃÉçÇøical Review Letters. "This result shows that when it comes to purifying entanglement, that's simply too good to be true."

The findings, he said, instead highlight the importance of tailoring noise-minimizing solutions to specific quantum systems.

Searching for solutions

To counteract the degradation of entangled states due to noise, scientists often use entanglement purification protocols (EPPs), which combine multiple imperfect entangled pairs to try to extract fewer pairs with less noise. But the team knew that certain systems are hard to cleanse of noise—often because the input states of EPPs are almost never identical in reality. Entanglement states vary based on how and when they are created, stored, and processed.

Graduate student Allen Zang from UChicago PME, and Xinan Chen from UIUC are the co-first authors of this paper.

"We knew that existing input-independent protocols are not guaranteed to improve the fidelity of the entangled states," said Zang.

"We wondered whether there was any possible protocol that could always guarantee improvements, a property we call universality," said Chen.

Zang, Chen and their colleagues began by tackling the question within a set of broadly-used EPPs, applying the protocols to known quantum operations. However, the idea of "universality" failed. Surprised, they broadened their analysis to all mathematically possible purification methods allowed under the rules of quantum mechanics.

Still, the result held: No universal EPP is guaranteed to improve fidelity of entangled states in all possible quantum systems.

"Importantly, we're not saying purification protocols don't work," said Eric Chitambar, Assoc. Professor of Electrical and Computer Engineering at UIUC. "But no single method works in all cases."

A fundamental limit

The work carries real implications for the design of quantum communication networks, where entangled states must be generated, stored, and transmitted over long distances. In these systems, blindly applying a purification protocol—without knowing the exact state of the system—can backfire.

Instead, the authors say, the results offer guidance: rather than seeking a universal solution, researchers should focus on tailoring error management strategies to the specific systems and error models they're working with.

"This result tells us not to waste time searching for a protocol that doesn't exist, and instead put more emphasis on understanding the unique characteristics of specific quantum systems," said Martin Suchara, Director of Product Management at Microsoft, one of the co-authors.

The team is now exploring how this kind of theoretical boundary might apply to other quantum resources. They're also investigating whether customized purification methods could still be developed for systems with well-understood errors—or whether a nearly universal method might exist under stricter constraints.