Quantum Shannon Information Theory -Design of communication, cipher and sensor-

TL;DR

This work surveys the evolution of quantum Shannon information theory from quantum communication foundations to capacity, reliability, and cipher applications. It covers the Holevo bound, SRM and collective/entangled measurements, and Lie‑algebra methods for noncommutative parameter estimation, illustrating how quantum effects can enhance communication and sensing. A central highlight is the KCQ‑based quantum stream cipher, which leverages quantum noise and secret key randomization to lift the Shannon impossibility bound and enable information‑theoretic security with short keys. The paper also explains reliability and cut‑off rate analyses for finite and continuous alphabets, and demonstrates sensor and memory‑reading techniques that surpass standard quantum limits. Together, these results indicate promising pathways for ultra‑fast, secure optical communications and advanced quantum sensing in practical networks.

Abstract

One of the key aspects of Shannon's theory is that it provides guidance for designing the most efficient systems, such as minimizing errors and clarifying the limits of coding. Such theories have made great developments in the 50 years since 1948. It has played a vital role in enabling the development of modern ultra-fast, stable, and highly dependable information and communication systems. The Shannon theory is supported by the statistical communication theory such as detection and estimation theory. The theory of communication systems that transmit Shannon information using quantum media is called quantum Shannon information theory, and research began in the 1960s. The theoretical formulation comparable to conventional Shannon theory has been completed. Its important role is to suggest that application of quantum effect will surpass existing communication performance. It would be meaningless if performance, efficiency, and utility were to deteriorate due to quantum effects, even if certain new function is given. This paper suggests that there are various limitations to utilizing quantum Shannon information theory to benefit real-world communication systems and presents a theoretical framework for achieving the ultimate goal. Finally, we introduce the perfect secure cipher that overcome the Shannon impossibility theorem without degrading communication performance and sensor et al as the examples.

Figures (12)

• Figure 1: Channel model in quantum Shannon information theory. Shannon information such as digital data or analog signal is transmitted by optical signal with quantum effect governed by quantum state. The quantum state and quantum measurement determine the communication performance. The existing functionality should not be degraded.
• Figure 2: Subject of consideration of quantum state transmission channel. The performance requirements for fiber optic communication are 100Gbit/sec to 100Tbit/sec as the transmission speed and a communication distance of 10,000km. For terrestrial spatial transmission, the speed is 1Gbit/sec to 10Gbit/sec and the communication distance is about 10km. There are no quantum states other than coherent states that satisfy these requirements. This is a consequence of Theorem 1.
• Figure 3: The fundamental concepts of quantum communication theory and quantum mathematical statistics are different, though both have certain similarities. The former must ensure technical superiority in conjunction with parameters such as communication speed (bit/sec), SNR, and bandwidth. The latter provides a formulation for statistics, with asymptotic properties etc. as its main objective. Thus, it does not provide the operational meaning. The relationship between the two is the same in classical theory.
• Figure 4: Effect for the decision operator based on entangled mesurement to reliablity function and cut off rate. Quantum Semiclass. Opt. vol-10, L7-L12, 1988.
• Figure 5: Numerical examples of reliabilty function and cut off rate for the decision operators based on entangled measurement and indivisual measurement.[38]