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The Secrets of Quantum Cryptography
July 29, 2011   
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A recent experiment by Polish physicists working at the National Laboratory for Quantum Technologies may help make quantum cryptography a more widespread technology.

In these times of massive data exchange, the confidentiality of transmitted information is of special importance. Quantum cryptography can ensure total privacy of transmission, according to researchers at the University of Warsaw’s Faculty of Physics.

Conventional quantum encryption methods rely on the use of particle sources in which certain particle properties are closely and ideally correlated—maximally entangled. A group of Polish physicists working at the National Laboratory for Quantum Technologies have experimentally demonstrated for the first time that even seemingly useless sources in which the entanglement of particles is substantially noisy, can be used for the secure transmission of a cryptographic key.

A cryptographic key is a random sequence of numbers used by the sender to encrypt information, and by the recipient to decrypt it. To enable both parties to exchange data confidentially, they need to have the same key, known only to them. Quantum cryptography is currently used for this very purpose: the secure transmission of a key between the sender and the recipient.

State of entanglement

In 1991, Polish physicist Artur Ekert developed the E91 quantum key distribution protocol using entangled quantum particles. Entanglement means that certain properties of the particles are correlated. For example, in a nonlinear crystal, pairs of polarization-entangled photons can be produced. This means that if the sender determines the vertical polarization of his photon, he can be confident that the second photon reaching the recipient is polarized horizontally. An analogous phenomenon occurs for any given pair of perpendicular directions. For the sender and recipient, the results of their own measurements appear to be completely random. But if they compare the two results, they will immediately notice that there are correlations between them resulting from the entanglement. This very mechanism is used in quantum cryptography.

If anyone attempted to eavesdrop on the transmission, they would destroy the entanglement, and the perfect correlations between the results of the sender and the recipient would disappear; the act of spying would be detected immediately, the researchers say.

But such a situation is the ideal case in which the entanglement between objects is maximal. In reality, entanglement is often submaximal, and the correlations between the results are imperfect and it becomes increasingly difficult to determine whether the message has been intercepted. In such a situation an “entanglement distillation” procedure is carried out as a routine practice to extract a certain number of maximally entangled states from noisy states.

There are, however, many states in which distillation of entanglement is impossible or highly inefficient. For a long time these states had been regarded unsuitable for quantum cryptography. But in 2005 a group of Polish physicists from Gdańsk showed theoretically that in certain situations the cryptographic key can be sent efficiently despite difficulties with distillation of entanglement.

Theory proved right

The researchers working at the National Laboratory for Quantum Technologies have checked the theory of the Gdańsk physicists in a carefully designed experiment. It was conducted by a team coordinated by Prof. Konrad Banaszek from the University of Warsaw Faculty of Physics, and Prof. Paweł Horodecki from the Gdańsk University of Technology Faculty of Technical Physics and Applied Mathematics. Krzysztof Dobek, a Ph.D. researcher working on an academic fellowship at the National Laboratory for Atomic, Molecular and Optical Physics at the Nicolaus Copernicus University in Toruń, was responsible for the experimental side of the project.

The experiment used a laser that emitted short pulses of light into a nonlinear crystal at a high frequency. Every now and again entangled particles emerged from the crystal. Most often these were pairs of photons (up to 6,000 per second), and far less often four entangled photons (only two per second). The electronic equipment was configured to record only the polarization of four entangled photons. In a four-day experiment, several hundred thousand such events were recorded.

The data analysis and the theoretical reconstruction of the quantum states were handled by Rafał Demkowicz-Dobrzański, Ph.D., and Michał Karpiński, M.Sc., both from the Faculty of Physics at the University of Warsaw. “A thorough analysis of the data from the experiment was particularly important in this case. We had to have statistical certainty that the generated quantum state was actually the state we wanted to obtain,” says Demkowicz-Dobrzański. It was demonstrated that, despite the noisy entanglement, each four entangled photons could be used to safely send an average of 0.7 bits of a cryptographic key.

Craving perfection

According to the researchers, the experiment may be of vital importance to practical quantum cryptography. Currently, only sources of pure, maximally entangled states are used in encryption. The experiment of the Polish physicists shows that in the future sources of entangled particles may be used to transmit a quantum cryptographic key even in situations where the generated entanglement is noisy and difficult to distill.

“The experiment has proven that the usefulness of entanglement sources in cryptography does not have to depend on their perfection,” said Prof. Banaszek. “If a new source produces a noisy entanglement but proves to be more efficient or cheaper than the currently used sources, we will nonetheless be able to use it successfully.”

An article describing the experiment and data analysis was published in a recent issue of the science journal Physics Review Letters. The research was conducted as part of the CORNER and Q-ESSENCE projects financed under the European Union’s 7th Framework Program, with the support of the TEAM program of the Foundation for Polish Science and the Polish Ministry of Science and Higher Education.
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