Information has a well-defined meaning in physics. The most fundamental analysis of the nature of information carried out so far originates from and in physics. In physics, the sub-discipline that comes closest to the derived meaning is communication theory. Originating traditionally as it does, communication theory concerns itself primarily with the challenge of information transmission rather than with the problems of information content or meaning. It is abstract in its approach to information, though concerned with the technical characteristics of communication channels independently of the nature of message sources, senders, receivers, or message destinations and coding strategies.
Information has a well-defined meaning in physics. The most fundamental analysis of the nature of information carried out so far originates from and in physics. In physics, the sub-discipline that comes closest to the derived meaning is communication theory. Originating traditionally as it does, communication theory concerns itself primarily with the challenge of information transmission rather than with the problems of information content or meaning. It is abstract in its approach to information, though concerned with the technical characteristics of communication channels independently of the nature of message sources, senders, receivers, or message destinations and coding strategies.
Founded by Shannon, information theory deals with the fundamental principles of communication. The two most important questions answered by this theory are how much we can compress a given data source and how much data we can transmit in a given communication channel. Information theory is essentially statistically minded. Data sources are modeled as random processes, and transmission channels are also modeled in probabilistic terms. The theory does not deal with the content of information – it deals with the frequency at which symbols (letters, figures, etc.) appear or are processed but not their meaning. A statistical model is not the only option. Non-statistical theories also exist (e.g., Kolmogorov complexity). However, in this section and throughout this book, we will only use the statistical tools. Information theory is of central importance in quantum cryptography. It may be used to model the transmission of the key elements from Alice to Bob. Note that what may happen on the quantum channel is better described using quantum information theory – see Chapter 4. Yet, the key elements chosen by Alice and those obtained by Bob after measurement are classical values so, for instance, the transmission errors can accurately be modeled using classical information theory. Reconciliation, in particular, requires classical information-theoretic techniques. Source coding Source coding is the first problem that information theory addresses. Assume that a source emits symbols x i from an alphabet χ and that it can be modeled by the random variable X on χ. For instance, the source can be the temperature measured by some meteorological station at regular intervals or the traffic on a network connection.
Scientific progress in physics and mathematics has led to the development of efficient technology for communicating and distributing information in the 20th century. This technology forms one of the cornerstones of information society and our global economy, which are highly reliant on secure methods to transfer and distribute information quickly. To satisfy ever-increasing demands for speed and security, encryption and communication methods are constantly improved and there is an ongoing effort to develop corresponding technology further. Classical information theory is not usually part of a physics undergraduate degree course. The theory assumes simple classical properties of physical systems and based on those a largely mathematical theory of information is established. The obtained results are independent of the chosen implementation and its physical details. However, one still has to acknowledge that information is physical, that is information carriers, senders, and receivers obey the laws of physics. The notion of quantum information comes about since it turns out that the rules of quantum mechanics violate some of the basic physics assumptions in classical information theory. The consequences of this are many, ranging from improved channel capacities, the possibility of physically secure communication protocols, to invalidating some beliefs about the security of classical communication protocols. So far the approach followed in this book was to assume idealized physical systemswhich perfectly implement qubits and then demonstrate how quantum computing algorithms can be realized using perfect qubits. Error correction and fault tolerance were only mentioned briefly.
Abstract. In the model of perfectly secure message transmission schemes (PSMTs), there are n channels between a sender and a receiver. An infinitely powerful adversary A may corrupt (observe and forge) the messages sent through t out of n channels. The sender wishes to send a secret s to the receiver perfectly privately and perfectly reliably without sharing any key with the receiver. In this paper, we show the first 2-round PSMT for n = 2t + 1 such that not only the transmission rate is O(n) but also the computational costs of the sender and the receiver are both polynomial in n. This means that we solve the open problem raised by Agarwal, Cramer and de Haan at CRYPTO 2006. The main novelty of our approach is to introduce a notion of pseudobasis to the coding theory. It will be an independent interest for coding theory, too.
Abstract Anonymous quantum communication (AQC) enables the secure transmission of quantum or classical messages between a sender and a receiver while ensuring the anonymity of their identities. Existing AQC protocols primarily address one-to-one anonymous communication. When there are multiple senders, they must send their messages sequentially to avoid collision problems. In this paper, we propose a multi-participant quantum anonymous communication (MQAC) by employing high-dimensional entangled states. In this protocol, multiple senders establish anonymous entanglement with multiple receivers of their choice and send quantum messages anonymously and simultaneously via quantum teleportation. To propose MQAC, we first present the toolbox we developed, which includes several sub-protocols such as the verification protocol, collision detection protocol, address distribution protocol, and notification protocol. These sub-protocols, which we propose, not only are important parts of MQAC but also serve as the foundation for solving many more complex tasks, such as anonymous commodity transaction. Additionally, the analysis of MQAC demonstrates that neither internal nor external attackers can steal the identities of the communication parties or the transmitted messages by employing any attack. Our work represents an original exploration of anonymous message transmission between multiple senders and receivers in quantum networks.
Introduction Quantum information theory is the study of how the peculiar features of quantum mechanics can be exploited for the purposes of information processing and transmission. A central theme of such a study is the ways in which quantum mechanics opens up possibilities that go beyond what can be achieved classically. This has in turn led to a renewed interest in, and a new perspective on, the differences between the classical and the quantum. Although much of the work along these lines has been motivated by quantum information theory – and some of it has been motivated by the conviction that quantum theory is essentially about possibilities of information processing and transmission – the results obtained, and the frameworks developed, have interest even for those of us who are not of that conviction. Indeed, much of the recent work echoes, and builds upon, work that predates the inception of quantum information theory. The significance of such work extends beyond the setting of quantum information theory; the work done on distinguishing the quantum from the classical in the context of frameworks that embrace both is something worthy of the attention of anyone interested in the foundational issues surrounding quantum theory. One of the striking features of quantum mechanics lies in its probabilistic character. A quantum state yields, not a definite prediction of the outcome of an experiment, but a probability measure on the space of possible outcomes. Of course, probabilities occur also in a classical context.
Ever since its invention in the 1920s, quantum physics has given rise to countless discussions about its meaning and about how to interpret the theory correctly. These discussions focus on issues like the Einstein-Podolsky-Rosen paradox, Quantum non-locality and the role of measurement in quantum physics. In recent years, however research into the very foundations of quantum mechanics has also led to a new field – quantum information technology. The use of quantum physics could revolutionize the way we communicate and process information.