Quantum particles are known to be strange or even “spooky.” But can those properties ever be useful? A new study proves that one type of wackiness—entanglement between identical particles—has practical value.

Ordinarily, two objects are never exactly alike. They can only seem that way because scientists use imperfect instruments to try and tell them apart. In quantum physics, however, true indistinguishability is possible. For example, while two distinguishable electrons may seem to be the same, they can often be differentiated by measuring their respective spins. For identical quantum particles, there is neither an analogous quantity that could be measured nor a more perfect measuring device that could discern some other difference between them.

Quantum particles can also be entangled. This type of connection is so strong that nothing about one of the entangled particles can be described without having to reference the other. Albert Einstein famously called quantum entanglement “spooky action at a distance,” because it somehow allows particles to always be “in touch,” no matter how far apart researchers locate them. Combining these two properties that are specific to quantum mechanics—true indistinguishability and entanglement—has so far only resulted in confusion among physicists.

Now researchers have mathematically quantified just how useful fully indistinguishable entangled particles can be. Their preprint study, which in August was accepted for publication in Physical Review X, shows that identical-particle entanglement can be the secret ingredient for improving today’s best recipes for quantum information processing. The finding could prove crucial for developing better materials, computers and telecommunications systems.

Real or Imaginary?

“There’s been a long discussion about the nature of identical-particle entanglement,” says Benjamin Morris, a physicist at the University of Nottingham in England and co-lead author of the study. In fact, some physicists have argued that such entanglement is nothing more than a quirk of mathematics. According to the rules of quantum mechanics, Morris explains, particles that are exactly the same are only allowed to make up very specific states. These states have a mathematical form equivalent to the one describing entangled particles that can be told apart through some measurement. But unlike such distinguishable particles, truly identical particles are assigned labels that do not reflect any physical difference between them. “You could argue that these labels have no meaning,” Morris admits.

Maciej Lewenstein, a physicist at the Institute of Photonic Sciences in Spain, who was not involved with the study, illustrates this point with an extreme example: a system consisting of two identical quantum particles—one inside your body, and the other on the moon. A mathematical description of their shared state suggests they are entangled. This result is automatic—essentially given “for free” because of quantum rules for indistinguishability rather than arising from some entangling protocol carried out by a researcher. But the implied connection between the particles has no obvious practical value. More commonly, physicists would take two particles that they know they can differentiate and purposefully entangle the pair. Only then would the scientists take one particle to the moon, allowing Einstein’s spookiness to guarantee that measuring some physical property of the other particle on Earth would instantaneously reveal the value of the same measurement for its lunar partner. But performing a measurement on one entangled identical particle does not reveal anything physically new about the other—the two are, after all, indistinguishable, on the moon or anywhere else.

Nevertheless, experimental physicists had noticed that systems of such particles could produce better results in certain experiments than their unentangled counterparts, notes Gerardo Adesso, a mathematical physicist at the University of Nottingham and a co-author of the new paper. “It seemed that this property was at least something useful,” he says. For example, using identical entangled particles led to better accuracy in quantum metrology, the quantum science of very precise measurements. In the study, Adesso, Morris and their collaborators determined that such improvements were made explicitly because of entangled identical particles rather than some other property of quantum mechanics. Morris offers an analogy: “Let’s say you baked a loaf of bread, and you want to know ‘What was it that made the bread rise?’” he says. “We showed that particle entanglement was the ‘yeast.’” The team’s result is the strongest evidence yet of identical particle entanglement being a feature of physical reality and not just a mathematical oddity.

A Quantum Test Kitchen

The researchers’ study relies on quantum resource theory. This idea involves selecting some specific quantum property of a system—such as identical particle entanglement—then measuring how that property enhances the system’s performance in some task, says Eric Chitambar, a quantum information researcher at the University of Illinois at Urbana-Champaign, who was not involved with the paper. Accordingly, the team first identified a set of states that exhibit identical particle entanglement (states containing “yeast” in Morris’s metaphor) and a set of operations for manipulating them (actions involved in “bread making”). An important constraint, Chitambar notes, is that any operation generating additional identical particle entanglement is forbidden. In the bread analogy, the researchers avoided operations akin to adding baking powder so that they could make clear statements about the importance of yeast already being in their dough. By working out just how much yeast produces a certain amount of “rise” in the system, they were able to quantify the effects of identical particle entanglement. In a final step, they checked the validity of their bread-making analysis by using it on the results from a previously conducted investigation that relied on identical particles, finding good agreement between their theory and the actual experiment.

The team also proved that systems with entangled identical particles can be coaxed into having other forms of entanglement that are already widely used in quantum computing. Jayne Thompson, a physicist at the Singapore-based company Horizon Quantum Computing, who was not affiliated with the study, explains this finding by likening identical-particle entanglement to “a valid currency” that can be exchanged for other operationally useful physical properties. As with any currency exchange, the precise exchange rate is important. Adesso offers one example: “The figure of merit that people use to quantify the advantages in metrology applications can actually be interpreted as a measure of the amount of [identical] particle entanglement,” he says. Because Adesso and his collaborators were able to produce concrete measures of the usefulness of identical-particle entanglement, they are optimistic their approach can be used to more rigorously quantify the varying performance of myriad quantum-information-processing systems—an important development to combat hype in this rapidly expanding field.

Far from being mere artifacts of wacky math, identical quantum particles are proving to be real, valuable assets for the future of quantum technology. “We hope the impact of this paper is to make the [physics] community reassess the value of identical particles in quantum mechanics more generally,” Adesso says.