A scalable approach to distill quantum features from higher-dimensional entanglement

The operation of quantum technologies relies on the reliable realization and control of quantum states, particularly entanglement. In the context of quantum physics, entanglement entails a connection between particles, whereby measuring one determines the result of measuring the other even when they are distant from each other, and in a way that defies any intuitive explanation.

A key challenge in the development of reliable quantum technologies is that entanglement is highly susceptible to noise (i.e., random interactions with the environment). These interactions with noise can adversely impact this desired quantum state of affairs and, in turn, reduce the performance of quantum technologies.

Researchers at Shandong University in China and National Cheng Kung University in Taiwan recently implemented a key step to experimentally recover hidden quantum correlations from higher-dimensional entangled states.

This method, outlined in a paper published in Physical Review Letters, entails the implementation of so-called single-copy local filtering (ScLF) operations.

“The preparation and manipulation of quantum entanglement are always imperfect, compromising their performance in quantum processing information tasks,” He Lu, co-senior author of the paper, told Phys.org.

“Although conventional distillation protocols promise to return at least one copy of maximal entanglement over multi-copy noisy states, it is not ‘friendly’ for photonic systems as the strong photon-photon interactions required for collective manipulation remain challenging.”

While physicists have developed various protocols for distilling entanglement over the past decades, most existing ones are difficult to implement on quantum systems comprised of photons (i.e., particles of light). The development of distillation approaches that are easier to implement on photonic systems could thus be highly advantageous, as it could inform quantum physics research and improve quantum technologies.

“The idea of single-copy distillation came out when I visited Liang in 2019, when he shared the thought of ‘activating the teleportation power with ScLF operation,'” said Lu. “I quickly realized this was the easy-to-implement distillation protocol I sought, naturally leading to our collaboration.”

The first objective of the recent study by Lu and his colleagues was to use ScLF to observe quantum features that were initially absent in a class of mixed quantum states known as Werner states, particularly nonlocality (i.e., the feature underpinning correlations between the behavior of entangled particles).

In addition, the researchers wanted to show that this technique is scalable and easier to implement on optical systems than existing entanglement distillation schemes.

“Our work is a natural continuation of our previous collaboration, aiming to recover teleportation power by ScLF,” Yeong-Cherng Liang, co-senior author of the paper, told Phys.org.

“A question left open there was why one should favor a qubit projection over other ScLFs. This led us to higher-dimensional Werner states—a widely discussed family of quantum states in quantum foundations and entanglement distillation—but whose nonlocality has never been demonstrated. We decided to take up this challenge, and there we go!”

To demonstrate the potential of their ScLFs-based approach for the distillation of quantumness, the researchers carried out a series of experiments utilizing a two-qutrit photonic system, in which each quantum unit (qutrit) can exist in a superposition of three states. They specifically prepared the three-dimensional Werner states, which were encoded in the degrees of freedom (DoF) of photon pairs.

“To this end, we first prepared a two-qubit Werner state encoded in the polarization DoF, then used an array of beam displacers and waveplates to transform the quantum information to the path DoF,” explained Lu. “The ScLF is quite simple—it only requires the blocking of one of the three paths.”

Lu, Liang and their colleagues also used theoretical frameworks to confirm that their technique was effective in distilling quantum correlations in their experiments. Their analyses demonstrated that despite imperfections in their experiments, the ScLF implemented did transform the states they prepared in the way they anticipated, allowing them to observe quantum features that were previously hidden.

“To this end, we checked the experimentally ‘reconstructed’ states against various criteria and, in some cases, also performed numerical optimizations to strengthen our claims,” said Liang.

The recent work by this team of researchers could significantly reduce the experimental complexity required to distill useful quantum features from noisy interactions. Notably, their experiments and theoretical analyses demonstrated that their proposed distillation approach is scalable and can also be applied to higher-dimensional quantum systems.

“To me, one of the most exciting moments is our rediscovery of the qubit decomposition of Werner states—implicitly given in the work of Popescu,” said Liang.

“Not only has this shed light on a question that has led us to this work—namely, why one should favor qubit projection over other ScLFs—but it has also facilitated the possibility for us to perform our experimental demonstration. As for achievement, I would pick the first proof-of-principle experimental validation of the nonlocality of higher-dimensional Werner states, 30 years after Popescu first noticed it.”

The new take on distillation advocated by He, Liang and their colleagues could soon be used to distill the quantumness in other higher-dimensional quantum systems, to further validate its potential. The team’s findings could also have interesting theoretical implications, as it challenges previous views suggesting that entanglement can only become useful when it is heavily “purified” from noise.

In his next studies, Liang, who is a theoretical physicist working at National Cheng Kung University and Deputy Director of the Center for Quantum Frontiers of Technology (QFort), plans to devise an even more efficient single-copy distillation-based protocol to extract genuine quantum features from Werner states or prove that the current protocol is already optimal.

Lu and his colleagues at Shadong University, on the other hand, hope to soon demonstrate the implementation of the new distillation protocol on quantum states with more dimensions.

“In this work, we have demonstrated the single-copy distillation on three-dimensional quantum states,” added Lu.

“I would like to explore even higher-dimensional states, although implementing our scheme using bulk optics in such cases seems quite challenging. However, the rapid development of integrated optics offers a promising platform for such demonstrations.”

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