Quantum information could be transmitted more efficiently thanks to a new protocol that uses nonlinear optics to transfer high-dimensional, spatially complex states of light. Developed by researchers in South Africa, Spain and Germany, the protocol is similar to quantum teleportation and relies on encoding information in the photons’ orbital angular momentum states.

Quantum communication protocols such as BB84 work by allowing two parties (generally known as Alice and Bob) to exchange encrypted information over an insecure link. To do this, they must share a resource of entangled states. Such states cannot be measured without destroying them, so a third party who does not share the entanglement cannot decrypt the information.

For this setup to work, however, the entangled states must first be generated and securely distributed to Alice and Bob. For perfect security, this distribution should occur via the sharing of single entangled particles. The original BB84 protocol proposed doing this by encoding entanglement in the polarization states of photons, but that only allows each particle to transmit a single bit of entanglement. Researchers have therefore sought more efficient options.

Spiralling wavefronts

One promising possibility is to use a different photon property, such as orbital angular momentum. This arises from the rotation of wavefronts like fusilli spirals. Each wavefront must rotate an integer number of times per wavelength to ensure that the wavefunction does not take multiple values at the same point in space, but in theory it is unbounded. Unlike polarization (which is given by the spin angular momentum quantum number) it therefore provides an infinite set of quantized, orthogonal states and an infinite-dimensional basis in which a photon’s field can be structured.

In the new work, which is described in Nature Communications, researchers led by Andrew Forbes of the University of the Witwatersrand demonstrate a protocol that, in principle, could allow Alice and Bob to transmit high-dimensional spatial information between them using a single photon and nonlinear optics. The protocol begins when Bob pumps a nonlinear crystal with a laser, causing it to (occasionally) produce a pair of entangled, lower-frequency photons with opposite orbital angular momenta via a mechanism called spontaneous parametric down conversion. One photon from each pair is sent to Alice, while Bob retains the other.

Alice, meanwhile, encodes the spatial information she wishes to transmit into the orbital angular momenta of photons emitted from her own laser. She directs these photons into a second nonlinear crystal, which also receives the photons from Bob. The photons from Bob carry no information, but when they enter Alice’s crystal, a small proportion of them undergo another nonlinear optical process called sum-frequency generation. This is effectively spontaneous parametric down conversion in reverse, allowing two photons to occasionally produce a single photon of higher frequency if the photons from Alice and Bob have equal and opposite angular momenta. When Alice reports such a high-frequency photon arriving in her detector, Bob measures the angular momentum of his photon.

Entanglement as a resource

Notably, this process does not achieve an “entanglement swap” of the kind required in a quantum repeater. For that, the photons entering the first crystal would need to become entangled with the photons coming out of the second, and the coherent state Alice sent into her crystal would need to be transferred directly onto the state of the photon remaining with Bob. This would require much greater efficiency in the up-conversion and down-conversion processes than is presently possible in the non-linear optics used here.

Instead, the researchers use the fact that, if a photon takes part in both down conversion and sum-frequency differentiation, the non-transmitted photons from Bob’s spontaneous parametric down-conversion process must have the same orbital angular momentum as the photons Alice used to encode spatial information. By measuring his own non-transmitted photon, therefore, Bob can decipher the information, but nobody who lacks this photon can do so. “We use the entanglement as a resource,” explains team member Adam Vallés of the Institute for Photonic and Optical Sciences in Barcelona.

Confidential information

The researchers believe their scheme, which they demonstrated in the laboratory using 15 different angular momenta for the photons, could produce a quantum-secure authentication system for banks and other entities. “Let’s say you have confidential information you want to send, it could be a fingerprint, an ID document or whatever,” says Forbes. “You have this photon that gets sent to you that makes our scheme work, you overlap this photon from Bob or the bank with the information that you want to send and you get a click in your detector. And when you do this, and you share that information with the bank, then the bank gets the information you want to send.”

Jonathan Leach, a quantum optics expert at the University of Heriot-Watt, UK, who was not involved in the research describes it as “a beautiful experiment and a very significant piece of work.” He adds, however, that the team’s paper, together with a similar work by researchers at China’s Xiamen University, sparked some controversy for the researchers’ initial claims that they had teleported high-dimensional quantum states. “At its heart, the spirit of quantum teleportation and any sort of teleportation is that you have some state that is transported to a new location and in that process the original is destroyed,” Leach says. This is not really true here, he adds, because Alice has to use a laser to generate many copies of the quantum state in order for one to undergo sum-frequency differentiation and be detected by Bob, so the original state is still present at Alice’s end.

Physicist Dan Gauthier of Ohio State University in the US is less enthusiastic, arguing that other groups have done similar work using less elaborate methods. He also sees a drawback in the protocol itself: “In the quantum parlance this is what’s called a projective measurement,” he says; “If the photon happens to be in the state you’re looking for see a click. If it’s not you gain no information. So if they have a d dimensional space the real benefit to what they’re doing is completely lost because every time they make a measurement there’s only a 1/d chance that they picked the correct mode in which to make it.” The researchers accept this criticism and are working to remedy it.

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• Source: https://physicsworld.com/a/new-protocol-transmits-quantum-information-in-complex-states-of-light/