# "Quantums" here and now (part 3)

In previous articles, I briefly talked about the premises in the development of quantum physics and computer science , which led to the emergence of quantum information and quantum computing as such. Today, I wanted to consider in this way another direction that has made a significant contribution:

In the 40s. Simultaneously with the development of computer science, fundamental changes took place in the understanding of the concept of communication. In 1948,

Shannon was interested in two key issues that are directly related to the exchange of information over the communication channel. First,

The quantum theory of information developed in approximately the same way. In 1995,

The classical ideas of error correction turned out to be very important and useful in the development and understanding of codes to correct quantum ones. In 1996,

This theory was developed with the aim of protecting quantum states from noise, but what about the transmission of classical information through a quantum channel? Is it effective at all, and if so, how much? And here a few surprises awaited. In 1992,

Even more questions and, accordingly, more interesting are the results in the field of

The classical theory of information begins with the study of the properties of a single communication channel, while in practice we often deal with a network of many channels, and not with one. The properties of just such networks are studied by the network theory of information, which has developed into an extensive and complex science.

The network quantum theory of information, on the contrary, is only in its infancy. So far, we know very little only about the possibilities of transmission in quantum networks, not to mention everything else. In recent years, a large number of results and developments have been obtained, even some quantum networks have been created, but a unified network theory for quantum channels has not yet existed. And here again everything rests on properties contradicting intuition, illustrating the strange nature of quantum information.

Thus, we can summarize the following result: everything is not at all smooth in the existing quantum information theory and there is still much to be worked out thoroughly. The key question remains the proof of a theorem similar to Shannon's coding theorem for a channel with noise. In addition, it is necessary to search for practically important problems for which distributed quantum computing has a significant advantage over distributed classical ones. Well, and as I said, it is necessary to create a unified network quantum theory of information, since we still hope to create some kind of more or less global quantum network. All this is the most important areas of research in this area.

*information theory*.## Information theory.

In the 40s. Simultaneously with the development of computer science, fundamental changes took place in the understanding of the concept of communication. In 1948,

*Claude Shannon*published several outstanding works, which laid the foundations of the modern theory of information and communication. Most likely, the most important step made by Shannon was that he introduced a mathematical definition of the concept of information. So try to think, based on the most simple, philistine considerations, on the following question: how would you approach the mathematical definition of the concept of “source of information?” Several solutions to this question appeared in the world at that time, but Shannon’s answer was the most fruitful in terms of improvement, understanding . Its use led to a number of certain serious results, and to the creation of a theory that adequately adequately reflects many real communication problems.Shannon was interested in two key issues that are directly related to the exchange of information over the communication channel. First,

*what resources are required to transmit information over a channel?*Secondly,*can information be transmitted in such a way as to be protected from noise in the communication channel?*And he answered both of these questions, proving two fundamental theorems. The first is*the coding theorem for a noise*-*free channel*, which determines the amount of physical resources required to store the output of an information source. The second is*the noise coding theorem.*- shows the amount of information that can be reliably transmitted over the channel in the presence of noise. Shannon has shown that error correction codes are possible in order to achieve reliable transmission in the presence of noise. Shannon's theorem for a channel with noise sets an upper limit on the protection of information provided by such codes. Unfortunately, the theorem does not give an explicit form of codes that help to reach this limit in practice. However, there is a complicated theory that allows you to develop good code that corrects errors. Such codes are widely used, for example, in computer modems and satellite communication systems.## Quantum Information Theory.

The quantum theory of information developed in approximately the same way. In 1995,

*Ben Schumacher*proved an analog of Shannon's theorem on coding in the absence of noise, along the way defining a quantum bit (qubit) as a real physical resource. But, it is worth noting that there is still no analogue of Shannon's coding theorem for a channel with noise as applied to quantum informatics. Despite this, a theory of correction of quantum errors was developed, which allows quantum computers to efficiently carry out calculations in the presence of noise, as well as reliably transmit information.The classical ideas of error correction turned out to be very important and useful in the development and understanding of codes to correct quantum ones. In 1996,

*Robert Culderbank*worked independently*with Peter Shore*and*Andrew Steen*discovered an important class of quantum codes, now called CSS codes based on the first letters of their surnames. Later, these codes were categorized as symplectic, or stabilizing, codes. These discoveries relied heavily on the ideas of the classical theory of linear coding, which significantly contributed to the quick understanding of the codes for correcting quantum errors and their further use in the field of quantum computing and quantum information.This theory was developed with the aim of protecting quantum states from noise, but what about the transmission of classical information through a quantum channel? Is it effective at all, and if so, how much? And here a few surprises awaited. In 1992,

*Charles Bennet and Steve Wisner*They explained to the world how to transmit two classical bits of information by transmitting only one qubit. This has been called super dense coding.Even more questions and, accordingly, more interesting are the results in the field of

*distributed quantum computing*. Imagine that you have two computers connected to a network on which some task is solved. How many network transmissions will it take to solve it? The answer to this question is not so important, something else is important. Not so long ago it was shown that for such a quantum system it may take an exponentially less amount of time to solve the problem than for classical network computers. This is definitely a very significant result, but there is one drawback - unfortunately, these tasks are not of particular interest in real conditions.## Network quantum information theory.

The classical theory of information begins with the study of the properties of a single communication channel, while in practice we often deal with a network of many channels, and not with one. The properties of just such networks are studied by the network theory of information, which has developed into an extensive and complex science.

The network quantum theory of information, on the contrary, is only in its infancy. So far, we know very little only about the possibilities of transmission in quantum networks, not to mention everything else. In recent years, a large number of results and developments have been obtained, even some quantum networks have been created, but a unified network theory for quantum channels has not yet existed. And here again everything rests on properties contradicting intuition, illustrating the strange nature of quantum information.

## Conclusion

Thus, we can summarize the following result: everything is not at all smooth in the existing quantum information theory and there is still much to be worked out thoroughly. The key question remains the proof of a theorem similar to Shannon's coding theorem for a channel with noise. In addition, it is necessary to search for practically important problems for which distributed quantum computing has a significant advantage over distributed classical ones. Well, and as I said, it is necessary to create a unified network quantum theory of information, since we still hope to create some kind of more or less global quantum network. All this is the most important areas of research in this area.