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# Quantum teleportation: the great discoveries of physicists

Quantum teleportation is one of the most important protocols in quantum information. Based on the physical resource of entanglement, it serves as the main element of various information tasks and is an important part of quantum technologies, playing a key role in the further development of quantum computing, networking and communication.

## From science fiction to the discovery of scientists

It has been more than two decades since the discovery of quantum teleportation, which, perhaps, is one of the most interesting and exciting consequences of the "strangeness" of quantum mechanics. Before these great discoveries were made, this idea belonged to the field of science fiction. Originally invented in 1931 by Charles H. Fort, the term "teleportation" has since been used to refer to the process by which bodies and objects are transferred from one place to another, in fact without overcoming the distance between them.

In 1993, an article was published describing the protocol of quantum information, called "quantum teleportation," which shared several of the above characteristics. In it, the unknown state of the physical system is measured and subsequently reproduced or "reassembled" in a remote location (the physical elements of the original system remain in the place of transmission). This process requires classical means of communication and excludes superluminal communication. It requires a resource of entanglement. In fact, teleportation can be considered as a protocol of quantum information, which most clearly demonstrates the nature of entanglement: without its presence, such a state of transmission would not be possible within the laws that describe quantum mechanics.

Teleportation plays an active role in the development of the science of information. On the one hand, this is a conceptual protocol that plays a decisive role in the development of formal quantum information theory, and on the other it is a fundamental component of many technologies. A quantum repeater is a key element of communication over long distances. Teleportation of quantum switches, calculations based on measurements and quantum networks - all are its derivatives. It is also used as a simple tool for studying "extreme" physics, relating to time curves and evaporation of black holes.

Today, quantum teleportation is confirmed in laboratories around the world using a variety of different substrates and technologies, including photonic qubits, nuclear magnetic resonance, optical modes, atomic groups, trapped atoms, and semiconductor systems. Outstanding results were achieved in the field of teleportation range, experiments with satellites are forthcoming. In addition, attempts have begun to scale to more complex systems.

## Teleportation of qubits

Quantum teleportation was first described for two-level systems, the so-called qubits. The protocol treats two remote parties, called Alice and Bob, who share 2 qubits, A and B, in a pure tangled state, also called the Bell pair. At the entrance of Alice another qubit is given, whose state ρ is unknown. Then it performs a joint quantum measurement called the Bell discovery. It carries a and A into one of Bell's four states. As a result, the state of the input qubit of Alice disappears during the measurement, and Bob's qubit is simultaneously projected onto P ^{†} _{k} ρP _{k} . At the last stage of the protocol, Alice passes the classical result of her measurement to Bob, who applies the Pauli operator P _{k} to restore the original ρ.

The initial state of the Alice qubit is considered unknown, since otherwise the protocol is reduced to its remote measurement. In addition, it itself can be part of a larger composite system shared with a third party (in which case successful teleportation requires the reproduction of all correlations with this third party).

A typical experiment on quantum teleportation assumes the original state to be pure and belonging to a limited alphabet, for example, six poles of the Bloch sphere. In the presence of decoherence, the quality of the reconstructed state can be quantitatively expressed by the teleportation accuracy F ∈ [0, 1]. This is the accuracy between the states of Alice and Bob, averaged over all the results of Bell's detection and the original alphabet. For small values of accuracy, there are methods that allow you to perform imperfect teleportation without using an intricate resource. For example, Alice can directly measure her initial state by sending the results to Bob to prepare the resulting state. This strategy of measurement-preparation is called "classical teleportation." It has the maximum accuracy F _{class} = 2/3 for an arbitrary input state, which is equivalent to the alphabet of mutually unbiased states, such as the six poles of the Bloch sphere.

Thus, a clear indication of the use of quantum resources is the accuracy value of F> F _{class} .

## Not a qubit of a single

According to quantum physics, teleportation is not limited to qubits, it can include multidimensional systems. For each finite measurement d, we can formulate an ideal teleportation scheme using the basis of the most tangled state vectors that can be obtained from the given maximally confused state and the basis {U _{k} } of unitary operators satisfying tr (U ^{†} _{j} U _{k} ) = dδ _{j, k} . Such a protocol can be constructed for any finite-dimensional Hilbert space of so-called. Discrete-variable systems.

In addition, quantum teleportation can also extend to systems with an infinite-dimensional Hilbert space, called continuously-variable systems. As a rule, they are realized by optical bosonic modes, whose electric field can be described by quadrature operators.

## Speed and the principle of uncertainty

What is the speed of quantum teleportation? The information is transmitted at a speed similar to the transmission rate of the same amount of classical - perhaps at the speed of light. Theoretically, it can be used in a way that the classical can not - for example, in quantum computing, where data is available only to the recipient.

Does quantum teleportation violate the principle of uncertainty? In the past, the idea of teleportation was not taken seriously by scientists, because it was believed that it violated the principle that prohibits any measuring or scanning process from extracting all information from an atom or other object. In accordance with the uncertainty principle, the more accurately the object is scanned, the more it is affected by the scanning process, until a point is reached when the original state of the object is broken to such an extent that it will no longer be possible to obtain enough information to create an exact copy. This sounds convincing: if a person can not extract information from the object to create an ideal copy, then the latter can not be done.

## Quantum teleportation for dummies

But six scientists (Charles Bennett, Gilles Brassard, Claude Crapo, Richard Josa, Asher Perez and William Wuthers) have found a way around this logic, using the famous and paradoxical feature of quantum mechanics, known as the Einstein-Podolsky-Rosen effect. They found a way to scan some of the information of the teleported object A, and the rest of the unverified part by means of the above effect to transfer to another object C, in contact with A never staying.

In the future, by applying an impact to C depending on the scanned information, you can enter C to state A before scanning. A itself is no longer in that state, as it is completely changed by the scanning process, so the result is teleportation, not replication.

## Struggle for range

- The first quantum teleportation was carried out in 1997 almost simultaneously by scientists from the University of Innsbruck and the University of Rome. During the experiment, the original photon having polarization and one of a pair of entangled photons underwent a change in such a way that the second photon received the polarization of the original photon. At the same time, both photons were at a distance from each other.
- In 2012, another quantum teleportation (China, University of Science and Technology) took place through a high-altitude lake for a distance of 97 km. A team of scientists from Shanghai, led by Juan Yin, managed to develop a suggestive mechanism that allowed to accurately target the beam.
- In September of the same year, a record quantum teleportation of 143 km was carried out. Austrian scientists from the Austrian Academy of Sciences and the University of Vienna, under the leadership of Anton Zeilinger, successfully passed quantum states between the two Canary Islands of La Palma and Tenerife. The experiment used two optical communication lines in the open space, a quantum and classical, frequency-uncorrelated polarization-confused pair of source photons, ultra-low noise single-photon detectors, and coupled clock synchronization.
- In 2015, researchers from the American National Institute of Standards and Technology for the first time transmitted information over a distance of more than 100 km by fiber. This became possible thanks to the single-photon detectors created at the Institute, using superconducting nanowires of molybdenum silicide.

It is clear that an ideal quantum system or technology does not yet exist and the great discoveries of the future lie ahead. Nevertheless, one can try to identify possible candidates in specific teleportation applications. A suitable hybridization, provided a compatible base and methods can provide the most promising future for quantum teleportation and its applications.

## Short distances

Teleportation for short distances (up to 1 m) as a subsystem of quantum computing is promising on semiconductor devices, the best of which is the QED scheme. In particular, superconducting transmonon qubits can guarantee deterministic and high-precision teleportation on a chip. They also allow direct feed in real time, which looks problematic on photonic chips. In addition, they provide a more scalable architecture and better integration of existing technologies compared to previous approaches, such as captured ions. At present, the only drawback of these systems seems to be their limited coherence time (<100 μs). This problem can be solved by integrating the QED scheme with semiconductor spin-ensemble memory cells (with nitrogen-substituted vacancies or rare-earth-doped crystals), which can provide a long coherence time for quantum data storage. At present, this implementation is the subject of much effort by the scientific community.

## City communication

Teleport communication in the city scale (several kilometers) could be developed using optical modes. With sufficiently low losses, these systems provide high speeds and bandwidth. They can be extended from desktop implementations to medium-range systems operating via ether or fiber, with possible integration with ensemble quantum memory. Longer distances, but at lower speeds, can be achieved using a hybrid approach or by developing good repeaters based on non-Gaussian processes.

## Long-distance communication

Long-distance quantum teleportation (more than 100 km) is an active area, but still suffers from an open problem. The polarization cubes are the best carriers for low-speed teleportation over long fiber-optic communication lines and over the air, but at the moment the protocol is probabilistic because of the incomplete detection of Bell.

Although probabilistic teleportation and entanglements are acceptable for tasks such as distillation of entanglement and quantum cryptography, this is clearly different from communication in which input information should be fully preserved.

If we take this probabilistic character, satellite implementations are within the reach of modern technologies. In addition to the integration of tracking methods, the main problem is the high losses caused by the spreading of the beam. This can be overcome in a configuration where entanglement is distributed from the satellite to terrestrial telescopes with a large aperture. Assuming a satellite aperture of 20 cm at 600 km altitude and 1 st telescope diaphragm on the ground, one can expect about 75 dB loss in the downlink channel, which is less than 80 dB of loss at ground level. Realizations of "earth-satellite" or "satellite-satellite" are more complicated.

## Quantum memory

The future use of teleportation as an integral part of a scalable network directly depends on its integration with quantum memory. The latter should have an excellent radiation-matter interface, in terms of conversion efficiency, recording and reading accuracy, storage time and bandwidth, high speed and storage capacity. First of all, this will allow using repeaters to extend communication far beyond direct transmission using error correction codes. The development of good quantum memory would allow not only to distribute network entanglement and teleportation communication, but also to process the stored information coherently. Ultimately, this can turn a network into an internationally distributed quantum computer or the basis for a future quantum Internet.

## Perspective developments

Atomic ensembles have traditionally been considered attractive due to their effective transformation of "light-matter" and their millisecond storage times, which can reach 100 ms, necessary for the transmission of light on a global scale. Nevertheless, more promising developments are expected today on the basis of semiconductor systems, where the excellent spin-ensemble quantum memory is directly integrated with the scalable architecture of the QED scheme. This memory not only can extend the coherence time of the QED circuit, but also provide an optic-microwave interface for the interconversion of optic-telecom and chip microwave photons.

Thus, the future discoveries of scientists in the field of the quantum Internet are likely to be based on long-range optical coupling, coupled with semiconductor nodes for processing quantum information.

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