We review the theory of compression of quantum information. In particular, compression of pure as well as mixed signal states is presented in unified framework. Open problems and perspectives are discussed.
This paper proposes a novel information compression algorithm leveraging quantum coherence as a fundamental resource. The core idea is to exploit the inherent properties of quantum systems – specifically quantum entanglement and superposition – to achieve compression efficiency exceeding that of classical methods. We introduce a framework wherein the degree of quantum coherence is directly correlated with the amount of information that can be reliably represented and subsequently compressed. The algorithm utilizes a series of quantum operations designed to manipulate and reduce the quantum state's coherence, effectively diminishing the information content while preserving the essential characteristics of the original data. We present a theoretical analysis demonstrating the potential for significant compression ratios and discuss the challenges and future directions of this approach. The primary focus is on establishing a quantifiable relationship between coherence and information density, a crucial step toward practical quantum information compression. We explore the mathematical foundations of this process, utilizing concepts from quantum information theory, and propose a preliminary algorithm outline.
This paper proposes a novel approach to entropy compression leveraging the unique properties of quantum entanglement. We demonstrate that, through the careful design of entangled states, it is possible to achieve compression rates exceeding those predicted by the classical Shannon limit. The core mechanism relies on encoding information within the quantum state distribution of an entangled state and exploiting the non-classical correlations inherent in entanglement for efficient probability distribution compression. Unlike traditional entropy compression methods which rely on statistical properties of classical information, our approach directly utilizes the correlations provided by entanglement, offering a fundamentally different strategy. We formulate the theoretical framework, outlining the key mathematical concepts and presenting a detailed analysis of the compression process. The central argument is that entanglement allows for a more effective representation of information than is possible with purely classical distributions, leading to a demonstrable advantage in compression. This work challenges the conventional understanding of entropy and compression, suggesting a new paradigm where quantum phenomena can be harnessed to surpass classical limitations. The presented model incorporates the concepts of entropy, entanglement entropy, and quantum state tomography to provide a comprehensive framework for this novel compression technique. The theoretical foundation is built upon the principles of quantum information theory, with a particular focus on the role of entanglement in information processing and storage. ---
This paper investigates a novel approach to quantum state compression and information extraction leveraging the inherent properties of quantum decoherence. The core concept involves utilizing the decoherence process itself as a tool for compressing quantum states while simultaneously extracting information preserved during this process. We demonstrate a theoretical framework wherein controlled decoherence can be harnessed to reduce the dimensionality of a quantum state, effectively compressing it, and simultaneously identify and isolate the information content that survives the decoherence. This work establishes a new perspective on quantum information processing, viewing decoherence not merely as a detrimental effect but as a potentially valuable resource for information manipulation. The proposed method offers a fundamentally different strategy for quantum state manipulation compared to traditional approaches, presenting a promising avenue for enhanced quantum state compression and information retrieval. The framework includes key mathematical formulations describing the decoherence process, state compression, and information extraction.
Recent advances in quantum simulation have enabled the discovery of novel forms of universality in quantum many-body dynamics. In this Review, we discuss deep thermalization and Hilbert space ergodicity--two recently discovered phenomena characterized by the emergence of distributions of quantum states that are "maximally random" in a precise sense. They offer a new perspective on how irreversible statistical mechanics arises from reversible unitary quantum dynamics, going beyond conventional theories of quantum thermalization and equilibration. We review a unifying framework, rooted in quantum information theory and principles of maximum entropy, that explains the different forms of ergodicity which arise under various physical constraints. We discuss open questions and active research directions, including generalizations beyond ensembles of pure quantum states, phase transitions in deep thermalization tied to deeper forms of ergodicity-breaking, connections to broader topics in quantum thermalization and ergodicity, and applications in quantum information science, such as for benchmarking or tomography.
This thesis addresses problems in the field of quantum information theory. The first part of the thesis is opened with concrete definitions of general quantum source models and their compression, and each subsequent chapter addresses the compression of a specific source model as a special case of the initially defined general models. First, we find the optimal compression rate of a general mixed state source which includes as special cases all the previously studied models such as Schumacher's pure and ensemble sources and other mixed state ensemble models. For an interpolation between the visible and blind Schumacher's ensemble model, we find the optimal compression rate region for the entanglement and quantum rates. Later, we study the classical-quantum variation of the celebrated Slepian-Wolf problem and the ensemble model of quantum state redistribution for which we find the optimal compression rate considering per-copy fidelity and single-letter achievable and converse bounds matching up to continuity of functions which appear in the corresponding bounds. The second part of the thesis revolves around information theoretical perspective of quantum thermodynamics. We start with a resource theory point of view of a quantum system with multiple non-commuting charges. Subsequently, we apply this resource theory framework to study a traditional thermodynamics setup with multiple non-commuting conserved quantities consisting of a main system, a thermal bath and batteries to store various conserved quantities of the system. We state the laws of the thermodynamics for this system, and show that a purely quantum effect happens in some transformations of the system, that is, some transformations are feasible only if there are quantum correlations between the final state of the system and the thermal bath.