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 component of quantum technologies, playing a key role in the further development of quantum computing, networks and communication.
From science fiction to the discovery of scientists
It has been more than two decades since the discovery of quantum teleportation, which is perhaps 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 realm of science fiction. First coined 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 without actually traveling the distance between them.
In 1993, an article was published describing the quantum information protocol, called"quantum teleportation", which shared several of the features listed above. In it, the unknown state of a physical system is measured and subsequently reproduced or "reassembled" at a remote location (the physical elements of the original system remain at the transmission site). This process requires classical means of communication and excludes FTL communication. It needs a resource of entanglement. In fact, teleportation can be seen as a quantum information protocol that most clearly demonstrates the nature of entanglement: without its presence, such a state of transmission would not be possible within the framework of the laws that describe quantum mechanics.
Teleportation plays an active role in the development of information science. On the one hand, it is a conceptual protocol that plays a decisive role in the development of formal quantum information theory, and on the other hand, it is a fundamental component of many technologies. The quantum repeater is a key element of communication over long distances. Quantum switch teleportation, dimension-based computing, and quantum networks are all derivatives of it. It is also used as a simple tool for studying "extreme" physics regarding time curves and black hole evaporation.
Today, quantum teleportation has been confirmed in laboratories around the world using many different substrates and technologies, including photonic qubits, nuclear magnetic resonance, optical modes, groups of atoms, trapped atoms, andsemiconductor systems. Outstanding results have been achieved in the field of teleportation range, experiments with satellites are coming. In addition, attempts have begun to scale up to more complex systems.
Teleportation of qubits
Quantum teleportation was first described for two-level systems, the so-called qubits. The protocol considers two distant parties, called Alice and Bob, who share 2 qubits, A and B, in a pure entangled state, also called a Bell pair. At the input, Alice is given another qubit a, whose state ρ is unknown. She then performs a joint quantum measurement called Bell detection. It takes a and A to one of the four Bell states. As a result, the state of Alice's input qubit disappears during the measurement, and Bob's B qubit is simultaneously projected onto Р†kρPk. At the last stage of the protocol, Alice sends the classical result of her measurement to Bob, who uses the Pauli operator Pk to restore the original ρ.
The initial state of Alice's qubit is considered unknown, because otherwise the protocol is reduced to its remote measurement. Alternatively, it may itself be part of a larger composite system shared with a third party (in which case, successful teleportation requires reproducing all correlations with that third party).
A typical quantum teleportation experiment assumes the initial state is pure and belonging to a limited alphabet,for example, the six poles of the Bloch sphere. In the presence of decoherence, the quality of the reconstructed state can be quantified by the teleportation accuracy F ∈ [0, 1]. This is the accuracy between Alice's and Bob's states, averaged over all Bell detection results and the original alphabet. At low accuracy values, there are methods that allow imperfect teleportation without using an obfuscated resource. For example, Alice can directly measure her initial state by sending the results to Bob to prepare the resulting state. This measurement-preparation strategy is called "classical teleportation". It has a maximum precision of Fclass=2/3 for an arbitrary input state, which is equivalent to an alphabet of mutually unbiased states, such as the six poles of a Bloch sphere.
Thus, a clear indication of the use of quantum resources is the accuracy value F> Fclass.
Not a single qubit
According to quantum physics, teleportation is not limited to qubits, it can include multidimensional systems. For each finite dimension d, one can formulate an ideal teleportation scheme using a basis of maximally entangled state vectors, which can be obtained from a given maximally entangled state and a basis {Uk} of unitary operators satisfying tr(U †j Uk)=dδj, k. Such a protocol can be constructed for any finite-dimensional Hilbertspaces of the so-called. discrete variable systems.
Besides, quantum teleportation can also be extended to systems with an infinite-dimensional Hilbert space, called continuous-variable systems. As a rule, they are realized by optical bosonic modes, the electric field of which can be described by quadrature operators.
Speed and uncertainty principle
What is the speed of quantum teleportation? Information is transmitted at a speed similar to that of the same amount of classical transmission - perhaps at the speed of light. Theoretically, it can be used in ways that the classical one cannot - for example, in quantum computing, where data is available only to the recipient.
Does quantum teleportation violate the uncertainty principle? In the past, the idea of teleportation was not taken very seriously by scientists because it was thought to violate the principle that any measuring or scanning process would not extract all the information of an atom or other object. According to the uncertainty principle, the more precisely an object is scanned, the more it is affected by the scanning process, until a point is reached where the original state of the object is violated to such an extent that it is no longer possible to obtain enough information to create an exact copy. This sounds convincing: if a person cannot extract information from an object to create a perfect copy, then the last one cannot be made.
Quantum teleportation for dummies
But six scientists (Charles Bennett, Gilles Brassard, Claude Crepeau, Richard Josa, Asher Perez and William Wuthers) found a way around this logic by using the famous and paradoxical feature of quantum mechanics known as the Einstein-Podolsky-Rosen effect. They found a way to scan part of the information of the teleported object A, and transfer the rest of the unverified part through the mentioned effect to another object C, which has never been in contact with A.
Further, by applying to C an influence that depends on the scanned information, you can put C into state A before scanning. A itself is no longer in the same state, as it has been completely changed by the scanning process, so what has been achieved 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, which has a polarization, and one of the pair of entangled photons, were changed in such a way that the second photon received the polarization of the original one. In this case, both photons were at a distance from each other.
- In 2012 another quantum teleportation took place (China, University of Science and Technology) through a high mountain lake at a distance of 97 km. A team of scientists from Shanghai, led by Huang Yin, managed to develop a homing mechanism that made it possible to accurately aim 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 UniversityVienna, led by Anton Zeilinger, successfully transferred quantum states between the two Canary Islands of La Palma and Tenerife. The experiment used two optical communication lines in open space, quantum and classical, frequency uncorrelated polarization entangled pair of source photons, ultra-low noise single-photon detectors and coupled clock synchronization.
- In 2015, researchers from the US National Institute of Standards and Technology for the first time transmitted information over a distance of more than 100 km via optical fiber. This became possible thanks to single-photon detectors created at the institute, using superconducting nanowires made of molybdenum silicide.
It is clear that the ideal quantum system or technology does not yet exist and the great discoveries of the future are yet to come. Nevertheless, one can try to identify possible candidates in specific applications of teleportation. Suitable hybridization of these, given a compatible framework and methods, could provide the most promising future for quantum teleportation and its applications.
Short distances
Teleportation over short distances (up to 1 m) as a quantum computing subsystem is promising for semiconductor devices, the best of which is the QED scheme. In particular, superconducting transmon qubits can guarantee deterministic and high-precision on-chip teleportation. They also allow real-time direct feed, whichlooks problematic on photonic chips. In addition, they provide a more scalable architecture and better integration of existing technologies compared to previous approaches such as trapped 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 circuit 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. This implementation is currently the subject of much effort from the scientific community.
City communication
Teleportation communication on a 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 over the air or fiber, with possible integration with ensemble quantum memory. Longer distances but lower speeds can be achieved with a hybrid approach or by developing good repeaters based on non-Gaussian processes.
Long distance communication
Long-distance quantum teleportation (over 100 km) is an active area, but still suffers from an open problem. Polarization qubits -the best carriers for low speed teleportation over long fiber links and over the air, but the protocol is currently probabilistic due to incomplete Bell detection.
While probabilistic teleportation and entanglements are acceptable for problems such as entanglement distillation and quantum cryptography, this is clearly different from communication, in which the input must be completely preserved.
If we accept this probabilistic nature, then satellite implementations are within the reach of modern technology. In addition to the integration of tracking methods, the main problem is high losses caused by beam spreading. This can be overcome in a configuration where entanglement is distributed from satellite to large aperture ground-based telescopes. Assuming a satellite aperture of 20 cm at 600 km altitude and a 1 m telescope aperture on the ground, about 75 dB of downlink loss can be expected, which is less than the 80 dB loss at ground level. Ground-to-satellite or satellite-to-satellite implementations are more complex.
Quantum memory
The future use of teleportation as part of a scalable network directly depends on its integration with quantum memory. The latter should have an excellent radiation-to-matter interface in terms of conversion efficiency, recording and reading accuracy, storage time and bandwidth, high speed and storage capacity. FirstIn turn, this will allow the use of relays to extend communication far beyond direct transmission using error correction codes. The development of a good quantum memory would allow not only to distribute entanglement over the network and teleportation communication, but also to process the stored information in a coherent manner. Ultimately, this could turn the network into a globally distributed quantum computer or the basis for a future quantum internet.
Promising developments
Atomic ensembles have traditionally been considered attractive due to their efficient light-to-matter conversion and their millisecond lifetimes, which can be as high as the 100ms needed to transmit light on a global scale. However, more promising developments today are expected based on semiconductor systems, where excellent spin-ensemble quantum memory is directly integrated with the scalable QED circuit architecture. This memory can not only extend the coherence time of the QED circuit, but also provide an optical-microwave interface for the interconversion of optical-telecom and chip microwave photons.
Thus, the future discoveries of scientists in the field of quantum internet are likely to be based on long-range optical communication coupled with semiconductor nodes to process quantum information.
