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arXiv · 2510.07726

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

Osamu Hirota
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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.

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Osamu Hirota. 2025-10-09. Quantum Shannon Information Theory -Design of communication, cipher and sensor-. https://arxiv.org/abs/2510.07726

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