Quantum cryptography using qutrits

Physicists from the University of Wien, Austria, are testing quantum cryptography (QC) systems based on qutrits instead of the more common qubits. These qutrits can simultaneously exist in three basic states. This means that QC systems based on qutrits will inherently be more secure.

Quantum cryptography (QC) is still in a very early stage and there are very few commercial products available. But this doesn't prevent researchers to look at new solutions. For example, physicists from the University of Wien, Austria, are testing qutrits instead of the more common qubits. These qutrits can simultaneously exist in three basic states -- instead of two for the qubits. This means that QC systems based on qutrits will inherently be more secure. But if QC using qubits has been demonstrated over distances exceeding 100 kilometers, the experiments with qutrits are today confined within labs. For more information, read this abstract of a highly technical paper or continue below.

Several research efforts are under way to look at high-dimensional quantum systems -- known as qudits. But this particular one has been conducted by the Quantum physics group of the University of Wien.It has been published by the New Journal of Physics under the name "Experimental quantum cryptography with qutrits." Here is an introduction from this paper.

In the last decades of the 20th century, cryptography schemes were proposed where the security relies on the laws of quantum mechanics. An intruder trying to listen in will always be detected. Because these schemes establish identical secret keys in two remote locations they have since become known under the term quantum key distribution (QKD).
QKD has been experimentally performed using all sorts of systems, applying various protocols, over distances of up to 120 km. These experiments are performed in the lab as well as in real-life environments, such as the nightly sky of a metropolitan city.

But now, researchers are testing higher-dimensional quantum systems (qudits), starting with qutrits. Why are they doing this?

For quantum cryptography the usage of higher-dimensional systems offers advantages such as an increased level of tolerance to noise at a given level of security and a higher flux of information compared to the qubit cryptography schemes. In general a QKD protocol is considered secure as long as the mutual information of the two parties A and B exchanging the key is greater than the mutual information of A and E (or B and E), where E is an eavesdropper.

As an example, you can see below a usage of quantum cryptography using qutrits (Credit: University of Wien).

Quantum cryptography using qutrits

[The above figure describes the] encryption and decryption of a short message sent between the two partners A and B using the error-corrected key obtained via the three-dimensional QKD. Three trits are sufficient to represent each letter of the alphabet plus the space character. An eavesdropper trying to intercept the message only gets random characters and hence cannot obtain any information on the original text, whereas observer B uses his key to decypher the original message.

If you're like me, you're probably scratching your head. How does this work? The researchers provide some -- highly technical -- explanations. Here is an excerpt.

The completely independent parties A and B produce keys secured by the violation of a three-dimensional Bell inequality by more than 4 standard deviations. The sifted keys had an error rate of approximately 10%. The effective key rate was rather low due to the slow motorized base change. This could be improved by implementing the base transformation with fast devices such as a spatial light modulator or electro-optical switches. In addition, with a biased choice of the positions of the transformation holograms, the key production rate could be further increased.

But as the physicists recognize in their conclusions, there are still many issues to solve before a QC system using qutrits -- or qudits -- can be used by ordinary people like you and me.

Sources: University of Wien, via New Journal of Physics, May 26, 2006

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