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Quantum resource theories from the viewpoint of statistical decision theory

文彬 周, Wenbin Zhou

Published Mar 25, 2021• 0 citations
OpenAlex

Abstract

Quantum phenomena are treated as resources for various real-world applications in quantum technologies.Comparing resources aims to discover the capability of quantum systems in information processing tasks.

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The field of quantum resource theory (QRT) has emerged as an invaluable framework for the examination of small and strongly correlated quantum systems, surpassing the boundaries imposed by traditional statistical treatments. The fundamental objective of general QRTs is to characterize these systems by precisely quantifying the level of control attainable to an experimenter. In this review article, we refrain from providing an exhaustive summary of the extensive literature on QRT. Rather, our focus centers on a specific subliterature founded upon the theory of majorization. The primary aim is to augment our comprehension of genuine quantum phenomena manifested across diverse technological applications and incite investigations into novel resource theories encompassing multiple types of resources. Consequently, we emphasize the underlying similarities shared by various resources, including bipartite quantum entanglement, quantum coherence, and superposition, alongside informational, thermal, and generalized nonequilibrium resources.
Quantum resources are certain features of the quantum world that provide advantages in certain information-theoretic, thermodynamic, or other useful operational tasks that are outside the realm of what classical theories can achieve. Quantum resource theories provide us with an elegant framework for studying these resources quantitatively and rigorously. While numerous state-based quantum resource theories have already been investigated, and to some extent, measurement-based resource theories have also been explored, instrument-based resource theories remain largely unexplored, with only a few notable exceptions. As quantum instruments are devices that provide both the classical outcomes of induced measurements and the post-measurement quantum states, they are quite important, especially for scenarios where multiple parties sequentially act on a quantum system. In this work, we study several instrument-based resource theories, namely (1) the resource theory of information preservability, (2) the resource theory of (strong) entanglement preservability, (3) the resource theory of (strong) incompatibility preservability, (4) the resource theory of traditional incompatibility, and (5) the resource theory of parallel incompatibility. Furthermore, we outline the hierarchies of these instrument-based resources and provide measures to quantify them. We then also established a relationship between our resource measure and the advantage in an information-theoretic task. In short, we provide a detailed framework for a wide variety of instrument-based quantum resource theories.
Quantum Reinforcement Learning (QRL) represents a groundbreaking approach at the intersection of quantum computing and artificial intelligence, promising to revolutionize decision-making processes across various domains. This chapter explores the fundamental principles of QRL and its diverse applications in critical sectors, including transportation networks, healthcare, financial decision-making, and smart energy systems. By leveraging the computational advantages of quantum algorithms, QRL enhances traditional reinforcement learning techniques, enabling more efficient data processing and improved strategic decision-making capabilities. Case studies within this chapter illustrate the transformative potential of QRL in optimizing logistics, improving medical imaging, and enhancing energy management strategies. The findings underscore the need for further exploration of quantum applications to fully harness their capabilities and address contemporary challenges. This comprehensive examination provides a solid foundation for researchers and practitioners aiming to integrate quantum technologies into real-world applications, paving the way for innovative solutions and sustainable advancements.