Answer to Question #341894 in Linear Algebra for Batman

Question

2. State at least 2 application of cryptography in engineering.

Answer 1

Cryptography – Quantum Keys

Many research groups around the world are developing devices for "restoring" quantum data — the so-called quantum repeaters, which are able to "revive" photons. A group of researchers from the Russian Quantum Center, led by Professor Alexander Lvovsky, found a way to restore the properties of photons and confirmed the operability of this method in an experiment. Scientists have been studying the phenomenon of quantum entanglement, in which the states of two or more objects — atoms, photons, ions — are connected. If the state of one of a pair of entangled photons is measured, then the state of the second one will immediately become definite, and the states of both of them will be uniquely connected — for example, if one photon is polarized vertically, then the second one is horizontally and vice versa.

"If you distribute pairs of entangled photons between two remote partners, then they both get the same sequence, which can be used as an encryption key, since this is a truly random sequence that cannot be guessed or calculated. If someone tries to spy on entangled photons, the correlation between them will be lost and it will no longer be possible to extract the key from them," explains Alexander Lvovsky.

The task is to preserve the state of quantum entanglement when transmitting over long distances. So far, there have been big problems with this. Until now , it has not been possible to transmit entangled photons over a distance of more than 100 km via fiber-optic networks . At large distances, quantum data is simply lost in noise. Conventional telecommunications networks use different types of repeaters or signal amplifiers that amplify the signal amplitude and remove noise, but in the case of quantum data, this approach does not work. The photon cannot be "amplified", when trying to measure its parameters, the state of the photon will change, which means that all the advantages of quantum cryptography disappear.

Quantum repeaters

Scientists from different countries are trying to develop the technology of quantum repeaters — devices capable of "recreating" quantum information without destroying it. Lvovsky's group seems to have found a way that can lead to success. Back in 2002, he and his colleagues discovered a curious effect that was called "quantum catalysis", by analogy with the chemical term, where certain reactions can only occur in the presence of a special substance — a catalyst. In their experiment, a light pulse was mixed with an "auxiliary" single photon on a partially light-transmitting mirror. Then this photon was "removed". It would seem that the state of the light pulse should not have changed. But, due to the paradoxical properties of quantum interference, the photon changed it in the direction of "strengthening" the quantum properties.

"At that time, this phenomenon looked like nothing more than a curious phenomenon, of which there are many in quantum physics. Now it turned out that it has an important practical application — it allows you to restore the entanglement of quantum states of light," says Alexander Lvovsky.

In their new work, the report of which was published in the journal Nature Photonics, scientists have learned to re-entangle "unraveled" photons. In the experiment, they used a nonlinear potassium titanyl phosphate crystal with a periodic domain structure as a source of entangled photons. It was "bombarded" with picosecond pulses of light generated by a titanium-sapphire laser. As a result, entangled pairs of photons were born in the crystal, which scientists sent to two different optical channels. In one of them, the light was subjected to a 20-fold attenuation with the help of darkened glass, as a result of which the level of entanglement dropped to almost zero. This corresponds to a loss level of 65 km of conventional fiber optic cable. Then the attenuated signal was sent to the beam splitter, where the quantum catalysis process took place. Scientists from the Lvovsky group call this process "quantum distillation", since fewer photons remain at the output, but their level of entanglement increases almost to the initial one. "Out of a million weakly entangled pairs of photons, one is strongly entangled. But at the same time, the correlation level is restored to the primary one, and although the data transfer rate is somewhat reduced, we can get a stable connection at a much longer distance," says Alexander Ulanov, a colleague of Lvovsky.