A common framework for quantum mechanics, thermodynamics and information theory is presented. It is accomplished by reinterpreting the mathematical formalism of Everett's many-worlds theory of quantum mechanics and augmenting it to include preparation according to a given ensemble. The notion of \emph{directed entanglement} is introduced through which both classical and quantum communication over quantum channels are viewed as entanglement transfer. This point is illustrated by proving the Holevo bound and quantum data processing inequality relying exclusively on the properties of directed entanglement. Within the model, quantum thermodynamic entropy is also related to directed entanglement, and a simple proof of the second law of thermodynamics is given.
A common framework for quantum mechanics, thermodynamics and information theory is presented. It is accomplished by reinterpreting the mathematical formalism of Everett's many-worlds theory of quantum mechanics and augmenting it to include preparation according to a given ensemble. The notion of \emph{directed entanglement} is introduced through which both classical and quantum communication over quantum channels are viewed as entanglement transfer. This point is illustrated by proving the Holevo bound and quantum data processing inequality relying exclusively on the properties of directed entanglement. Within the model, quantum thermodynamic entropy is also related to directed entanglement, and a simple proof of the second law of thermodynamics is given.
A union of quantum mechanics, thermodynamics and information theory is presented. It is accomplished by reinterpreting the mathematical formalism of Everett’s many-worlds theory of quantum mechanics and augmenting it to include preparation according to a given ensemble. The notion of directed entanglement is introduced through which both classical and quantum communication over quantum channels are reduced to entanglement transfer. The paradox of constant thermodynamic entropy in a closed quantum system is resolved. The view taken in this Letter is that the totality of conceptual experience can be described in terms of correlated random variables. This will allow us to make contact with Shannon’s information theory [1] in which random variables are the carriers of information. Two protagonists sharing the same physical world is no more than classical correlations between the states of their knowledge regarding that world. Similarly, the observation of definite physical laws is no more than classical correlations between states of knowledge regarding two consecutive acts of measurement, or preparation and measurement, depending on the experiment. For instance, a ball kicked by Alice seen as obeying Newton’s deterministic laws of motion is merely a statement about the correlation
Abstract This chapter discusses the principles of quantum information. The quantum mechanical equivalent of the Shannon noisy-channel communication theorem is obtained, along with some profound statements about the behavior of quantum information during generalised quantum measurements. The latter are very important in studies of quantum entanglement, but also in exploring the connections between thermodynamics, information theory, and quantum physics. This chapter also discusses equalities and inequalities related to entropy, the Holevo bound, capacity of a bosonic channel, information gained through measurements, relative entropy and thermodynamics, entropy increase due to erasure, and Landauer's erasure and data compression.
We investigate fundamental connections between thermodynamics and quantum information theory. First, we show that the operational framework of thermal operations is nonequivalent to the framework of Gibbs-preserving maps, and we comment on this gap. We then introduce a fully information-theoretic framework generalizing the above by making further abstraction of physical quantities such as energy. It is technically convenient to work with and reproduces known results for finite-size quantum thermodynamics. With our framework we may determine the minimal work cost of implementing any logical process. In the case of information processing on memory registers with a degenerate Hamiltonian, the answer is given by the max-entropy, a measure of information known from quantum information theory. In the general case, we obtain a new information measure, the "coherent relative entropy", which generalizes both the conditional entropy and the relative entropy. It satisfies a collection of properties which justifies its interpretation as an entropy measure and which connects it to known quantities. We then present how, from our framework, macroscopic thermodynamics emerges by typicality, after singling out an appropriate class of thermodynamic states possessing some suitable reversibility property. A natural thermodynamic potential emerges, dictating possible state transformations, and whose differential describes the physics of the system. The textbook thermodynamics of a gas is recovered as well as the form of the second law relating thermodynamic entropy and heat exchange. Finally, noting that quantum states are relative to the observer, we see that the procedure above gives rise to a natural form of coarse-graining in quantum mechanics: Each observer can consistently apply the formalism of quantum information according to their own fundamental unit of information.
Quantum teleportation, a cornerstone of quantum information science, has traditionally been viewed through the lens of quantum mechanics, focusing on the transfer of quantum states without physical transport. This paper proposes a novel interpretation of quantum teleportation as a quantum entanglement thermodynamics process. We argue that teleportation can be understood as an entropy-driven process mediated by quantum entanglement, where the transfer of quantum information is fundamentally linked to the increase of entropy in a larger system, adhering to the principles of the second law of thermodynamics. Specifically, we formulate the process mathematically, utilizing concepts like entanglement entropy, von Neumann entropy, and the Landauer principle to quantify the changes in thermodynamic properties during the teleportation event. We explore how the conservation of energy and the constraints imposed by the second law govern the successful completion of teleportation, providing a new framework for understanding and potentially controlling this remarkable quantum phenomenon. The central contribution of this work is to bridge the gap between quantum mechanics and thermodynamics, offering a richer and more fundamental perspective on quantum teleportation.
Abstract This book deals with the basic concept of information, its importance, and the similarities and differences between classical and quantum information. First, classical information theory and its application to communication are discussed. Quantum mechanics and communication based on the laws of quantum mechanics are then considered. Quantum entanglement, a key resource in quantum communication, is analysed both from the fundamental perspective and from the perspective of its information-processing capability. This book also introduces quantum computation (in the context of the search and factorisation algorithms) and the basics of quantum error correction. Throughout this book, the connections between information theory, thermodynamics, and (quantum) physics are emphasised and discussed. Other topics covered in the book are data compression, related measures of information such as relative entropy, joint entropy, conditional entropy, and mutual information, along with the capacity of a noisy channel.
This paper proposes a novel approach to quantum information transfer, termed "Quantum Entanglement Entropy Transfer (EET)." The core claim is that by precisely controlling the micro-scale entropy transfer between entangled particles, direct quantum information transmission can be achieved without relying on physical media, circumventing the limitations imposed by classical communication bottlenecks. The proposed mechanism utilizes non-classical thermodynamics and a specifically designed "entropy pump" system. This system leverages microscopic thermal fluctuations within entangled particles to facilitate non-local entropy transfer, thereby driving changes in the entanglement correlation between the particles. Mathematical formalism is presented to describe the entropy transfer process, highlighting the role of entanglement entropy and the thermodynamic parameters governing the system. The novelty of this approach lies in its utilization of entanglement as the primary medium for entropy transfer, coupled with the practical demands of quantum information transmission. The theoretical framework presented offers a potentially transformative pathway for quantum communication, moving beyond conventional approaches and opening avenues for ultra-fast, secure information transfer.