As semiconductor technology is rapidly approaching physical barriers that restrict the speed of digital signal processing, knowledge about physical limits to data transmission and processing is gaining more and more importance. This paper addresses a fundamental physical limit that derives from energy-time uncertainty. By relating the physical limitation to the basics of signal processing and information theory it turns out that trivalent signaling might become optimal at the frontiers of physics.
As semiconductor technology is rapidly approaching physical barriers that restrict the speed of digital signal processing, knowledge about physical limits to data transmission and processing is gaining more and more importance. This paper addresses a fundamental physical limit that derives from energy-time uncertainty. By relating the physical limitation to the basics of signal processing and information theory it turns out that trivalent signaling might become optimal at the frontiers of physics.
Information and computation theory have undergone a spurt of new growth, and a renewal of their historic connection to basic physics, as they have expanded to treat the intact transmission and processing of quantum states, and the interaction of such 'quantum information' with traditional forms of information. We may wonder why this did not happen earlier, as quantum principles have long been accepted as fundamental to all of physics. Perhaps the founders of information and computation theory, such as Shannon, Turing and von Neumann, were too accustomed to thinking of information processing in macroscopic terms, not yet having before them the powerful examples of the genetic code and ever-shrinking microelectronics. Be that as it may, information until recently has largely been thought of in classical terms, with quantum mechanics playing a supporting role in the design of the equipment to process it, and setting limits on the rate at which it could be sent through certain channels. Now we know that a fully quantum theory of information and information processing offers, among other benefits, a brand of cryptography whose security rests on fundamental physics, and a reasonable hope of constructing quan- tum computers that could dramatically speed up the solution of certain mathematical problems. These benefits depend on distinc- tively quantum properties such as uncertainty, interference and entanglement. At a more fundamental level, it has become clear that an information theory based on quantum principles extends and completes classical information theory, just as complex numbers extend and complete the reals. Besides quantum generalizations of classical notions such as sources, channels and codes, the new theory includes two complementary, quantifiable kinds of information— classical information and quantum entanglement. Classical infor- mation can be copied at will, but can only be transmitted forward in time, to a receiver in the sender's forward light cone. Entanglement in contrast, cannot be copied, but can connect any two points in space-time. Conventional data processing operations destroy entanglement, but quantum operations can create it and use it for various purposes, such as speeding up certain classical computa- tions and assisting in the transmission of classical information or intact quantum states. Part of the new quantum information theory is the qualitative and quantitative study of entanglement, and its interactions with classical information. Any means, such as an optical fibre, of delivering quantum systems more or less intact from one place to another, may be viewed as a quantum channel. Unlike classical channels, which are well characterized by a single capacity, quantum channels have several distinct capacities, depending on what one is trying to use them for, and what auxiliary resources are brought into play. New effects involving quantum information continue to be discovered, not only in the traditional areas of computation, channel capacity, and cryptography, but in areas such as commu- nication complexity and game theory.
The rapid development of the digital era and the increasing demands of information technologies create a need to create more reliable, secure and efficient communication systems. In this context, quantum signals represent a technology of the future that responds to the challenges that classical signal systems can no longer cope with — for example, the highest level of information security, accuracy and transmission speed. The use of quantum entanglement, superposition and correlations makes it possible to protect and process information at the highest level. Accordingly, the implementation of quantum signals is critically important for areas such as quantum communication, secure cyberinfrastructure, high-tech sensors and quantum computing systems. The paper reviews the role of quantum signals in modern technologies and their potential in the near future. Quantum signal theory combines the principles of quantum physics, information theory and signal processing. These features provide the highest accuracy in information transmission and processing, which is especially important in the development of quantum communication, quantum radars, and quantum sensors. This paper reviews the theoretical foundations of quantum signals, basic models, and their potential applications in modern technologies.
Many of the fundamental limits on information processing, from thermodynamics, relativity, and quantum mechanics, are only a few decades away. Novel physically motivated computing paradigms, such as reversible computing and quantum computing, may help in certain ways, but even they remain subject to some basic limits. One can arrive at several firm conclusions regarding upper bounds on the limits of computing. In this article, the author only reviews the fundamental technology-independent limits.
The study of quantum signals is one of the fundamental and strategic directions of telecommunications and engineering sciences, as it is directly related to the in-depth understanding of the laws of matter and energy at the microscopic level and the transition to a new stage of telecommunications systems, as well as the formation of new principles of information transmission and processing and the development of technological innovations. A quantum signal, as a physical object carrying a quantum state, be it a photon, an electron, a qubit localized in a superconducting circuit, or an atomic spin system, contains information encoded through superposition and quantum entanglement. It is thanks to these properties that it becomes possible to perform tasks that are either practically inaccessible or extremely resource-intensive within the framework of classical physics. For example, computational models based on the principles of quantum mechanics provide the basis for quantum systems, which potentially radically change the speed and efficiency of data processing, while quantum communication provides fundamentally secure channels for information transmission, which is especially important in light of modern cybersecurity challenges. Comparative studies of quantum signals in cryogenic and non-cryogenic environments provide important theoretical results.
The concept of physical layer security builds on the pivotal idea of turning the channel's imperfections, such as noise and fading, into a source of security. This is established through appropriately designed coding techniques and signal processing strategies. In this vein, it has been shown that fading channels can enhance the transmission of confidential information and that a secure communication can be achieved even when the channel to the eavesdropper is better than the main channel. However, to fully benefit from what fading has to offer, the knowledge of the channel state information at the transmitter (CSIT) is of primordial importance. In practical wireless communication systems, CSIT is usually obtained, prior to data transmission, through CSI feedback sent by the receivers. The channel links over which this feedback information is sent can be either noisy, rate-limited, or delayed, leading to CSIT uncertainty. In this paper, we present a comprehensive review of recent and ongoing research works on physical layer security with CSIT uncertainty. We focus on both information theoretic and signal processing approaches to the topic when the uncertainty concerns the channel to the wiretapper or the channel to the legitimate receiver. Moreover, we present a classification of the research works based on the considered channel uncertainty. Mainly, we distinguish between the cases when the uncertainty comes from an estimation error of the CSIT, from a CSI feedback link with limited capacity, or from an outdated CSI.