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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