Encrypted qubits can be cloned and stored in multiple locations without violating the no-cloning theorem of quantum mechanics, researchers in Canada have shown. Their work could potentially allow quantum-secure cloud storage, in which data can be stored on multiple servers, thereby allowing for redundancy without compromising security. The research also has implications for quantum fundamentals.

Heisenberg’s uncertainty principle – which states that it is impossible to measure conjugate variables of a quantum object with less than a combined minimum uncertainty – is one of the central tenets of quantum mechanics. The no-cloning theorem – that it is impossible to create identical clones of unknown quantum states – flows directly from this. Achim Kempf of the University of Waterloo explains, “If you had [clones] you could take half your copies and perform one type of measurement, and the other half of your copies and perform an incompatible measurement, and then you could beat the uncertainty principle.”

No-cloning poses a challenge those trying to create a quantum internet. On today’s Internet, storage of information on remote servers is common, and multiple copies of this information are usually stored in different locations to preserve data in case of disruption. Users of a quantum cloud server would presumably desire the same degree of information security, but no-cloning theorem would apparently forbid this.

Signal and noise

In the new work, Kempf and his colleague Koji Yamaguchi, now at Japan’s Kyushu University, show that this is not the case. Their encryption protocol begins with the generation of a set of pairs of entangled qubits. When a qubit, called A, is encrypted, it interacts with one qubit (called a signal qubit) from each pair in turn. In the process of interaction, the signal qubits record information about the state of A, which has been altered by previous interactions. As each signal qubit is entangled with a noise qubit, the state of the noise qubits is also changed.

Another central tenet of quantum mechanics, however, is that quantum entanglement does not allow for information exchange. “The noise qubits don’t know anything about the state of A either classically or quantum mechanically,” says Kempf. “The noise qubits’ role is to serve as a record of noise…We use the noise that is in the signal qubit to encrypt the clone of A. You drown the information in noise, but the noise qubit has a record of exactly what noise has been added because [the signal qubits and noise qubits] are maximally entangled.”

Therefore, a user with all of the noise qubits knows nothing about the signal, but knows all of the noise that was added to it. Possession of just one of the signal qubits, therefore, allows them to recover the unencrypted qubit. This does not violate the uncertainty principle, however, because decrypting one copy of A involves making a measurement of the noise qubits: “At the end of [the measurement], the noise qubits are no longer what they were before, and they can no longer be used for the decryption of another encrypted clone,” explains Kempf.

Cloning clones

Kempf says that, working with IBM, they have demonstrated hundreds of steps of iterative quantum cloning (quantum cloning of quantum clones) on a Heron 2 processor successfully and showed that the researchers could even clone entangled qubits and recover the entanglement after decryption. “We’ll put that on the arXiv this month,” he says.

 The research is described in Physical Review Letters and Barry Sanders at Canada’s University of Calgary is impressed by both the elegance and the generality of the result. He notes it could have significance for topics as distant as information loss from black holes: “It’s not a flash in the pan,” he says; “If I’m doing something that is related to no-cloning, I would look back and say ‘Gee, how do I interpret what I’m doing in this context?’: It’s a paper I won’t forget.”

Seth Lloyd of MIT agrees: “It turns out that there’s still low-hanging fruit out there in the theory of quantum information, which hasn’t been around long,” he says. “It turns out nobody ever thought to look at this before: Achim is a very imaginative guy and it’s no surprise that he did.” Both Lloyd and Sanders agree that quantum cloud storage remains hypothetical, but Lloyd says “I think it’s a very cool and unexpected result and, while it’s unclear what the implications are towards practical uses, I suspect that people will find some very nice applications in the near future.”

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As with people, age in cosmology does not always extrapolate. An early-career politician may be more likely to win a debate with a student than with a seasoned diplomat, but put all three in a room with a toddler and the toddler will almost certainly get their own way – they are following a different set of rules. A team of global collaborators noticed a similar phenomenon when peering at a cluster of developing galaxies from a time when the universe was just a tenth of its current age.

Cosmological theories suggest that such infant clusters should host much cooler and less abundant gas than more mature clusters. But what the researchers saw was at least five times hotter than expected – apparently not abiding by those rules.

“That’s a massive surprise and forces us to rethink how large structures actually form and evolve in the universe,” says first author Dazhi Zhou, a PhD candidate at the University of British Columbia.

Eyes on the past

Looking into distant outer space allows us to peer into the past. The protocluster of developing galaxies that Zhou and collaborators investigated – known as SPT2349–56 – is 12.4 billion light years away, so the light observed from it left home when the universe was just 1.4 billion years old. Light from so far away will be quite faint and hard to detect by the time it reaches us, so the researchers used the Atacama Large Millimeter/submillimeter Array (ALMA) to study SPT2349–56 using a special type of shadow.

As this type of protocluster develops, Zhou explains, the gas around its galaxies  becomes so hot that electrons in the gas interact with, and confer some of their energy upon, passing photons. This leaves light passing through the gas with more photons at the higher energy end of the spectrum and fewer at the lower end. When viewing the cosmic microwave background radiation – the “afterglow” left behind by the Big Bang – this results in a shadow at low energies. This energy shift, discovered by physicists Rashid Sunyaev and Yakov Zeldovich, not only reveals the presence of the protocluster, but the strength of this signature indicates the thermal energy of the gas in the protocluster.

The team’s observations were not easy. “This shadow is actually pretty tiny,” Zhou explains. In addition, there is thermal emission from the dust inside galaxies at radio wavelengths, originally estimated to be 20 times stronger than the Sunyaev–Zeldovich signature. “It really is like finding a needle in a haystack,” he adds. Nonetheless, the team did identify a definite Sunyaev–Zeldovich signature from SPT2349–56, with a thermal energy indicating that it was at least five times hotter than expected – thousands of times hotter than the surface of our Sun.

Time to upgrade?

SPT2349–56 has some quirks that may explain its high thermal energy, including three supermassive black holes shooting out jets of high-energy matter – a known but rare phenomenon for these supermassive black holes. However, simulations that take these outbursts into account as a heating mechanism that’s more efficient and occurs much earlier than heating from gravitational collapse (as current models suggest) still do not give the high temperatures observed, perhaps pointing to gaps in our knowledge of the underlying physics.

Eiichiro Komatsu from the Max-Planck-Institut für Astrophysik describes the work as “a wonderful  measurement”. Although not directly involved in this research, Komatsu has also looked at what the Sunyaev–Zeldovich effect can reveal about the cosmos. “The amount of thermal energy measured by the authors is staggering, yet its origin is a mystery,” he tells Physics World. He suggests these results will motivate further observations of other systems in the early universe.

“We need to be cautious rather than making any big claim,” adds Zhou. This is the first Sunyaev–Zeldovich detection of a protocluster from the first three billion years of the universe’s existence. Next, he aims to study similar protoclusters, and he hopes others will also work to corroborate the observations.

The research is reported in Nature.

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