A3/What is (quantum-) communication?

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Before considering the problem of cryptography, we want to address the general question of communication. We will use the term communication for any situation, in which some information is transferred from one party to another. For the rest of the section we will only consider situation in which information flows in one direction, so there is always one sender and one receiver of information.

Forms of communication

In the classical world it is usually not so important, in which form information is transmitted. The variety of forms used include sound waves (spoken language), electromagnetic waves (mobile communication, radio, optical fibres, sign language), variations in the surface of a medium (letter, print), electrical signals (email) and many more. In most communication scenarios many of these media are used and the information is transformed from one medium to another many times. If two people would, for instance, communicate using mobile phones, information would start as a sound wave, be converted into an electrical signal by the microphone, then transformed into electromagnetic signals, travel to the nearest mobile communication antenna, would there be transformed into an optical signal, travel via glass fibre to an antenna near the recipient and then the process would be reversed until the recipient will hear the sound waves produced by his telephone’s speaker. During all conversions the information does not change, apart from possible unwanted noise and errors during the communication. One calls any route on which information travels a communication channel. The cannel is called ideal, if any information can pass the channel unchanged. In the example the channel would be ideal if the recipient is unable to distinguish whether he uses a telephone or directly talks to the sender.

How to quantify information

In the technical communication we consider, all information is given in a form that can be quantified. The basic example are the letters, that for a sentence. The order of letters (and punctuation marks) will form the information that is to be transmitted during communication. The communication is successful, if all letters can be reconstructed by the receiver in the correct order. We do not consider so called “meta information“ here, like e.g. the pitch of the voice of one reads out the sentence. Of course, the spoken sentence could be recorded and converted into digital information, and then this information would be quantified again. This notion of information goes back to the work of Claude E. Shannon [ref].

Let us fix some notation: Communication is the process in which a sender transmits information to a receiver. This is done by transmitting signals that are interpreted by the receiver. The transformation of information into signals is also called encoding, while the opposite is called decoding. We will follow a convention in communication theory by giving names to the communicating parties. We call the sender Alice and the receiver Bob, the corresponding systems A and B. We have sketched the system in Fig. 1. The way through with the signals travel is called a cannel. In real life, communication channels tend not to be ideal, but noisy. This noise will lead to errors in the decoded information. For a reliable communication system is desirable to use an encoding/decoding scheme that is resistant against the typical channel noise.

What is quantum information?

Until now, we have only introduces an abstract concept of information, where the physical carrier of the information is not important. In contrast to that, quantum information can only by carried by quantum signals, i.e., by physical systems that can only be described by quantum physics. The terminology here is borrowed from the classical case, e.g., if Alice is able to transmit quantum systems to Bob, they have a quantum channel. To be more precise in the definition, we will next explain, how the different kinds of information can be modelled in mathematical terms.