A new interpretation of entanglement entropy is proposed: entanglement entropy of a pure state with respect to a division of Hilbert space into two subspaces 1 and 2 is an amount of information which can be transmitted through 1 and 2 from a system interacting with 1 to another system interacting with 2. The transmission medium is the quantum entanglement between 1 and 2. In order to support the interpretation, suggestive arguments are given: variational principles in entanglement thermodynamics and quantum teleportation. It is shown that a quantum state having maximal entanglement entropy plays an important role in quantum teleportation. Hence the entanglement entropy is, in some sense, an index of the efficiency of quantum teleportation. Finally, the implications for the information loss problem and Hawking radiation are discussed.
A new interpretation of entanglement entropy is proposed: entanglement entropy of a pure state with respect to a division of Hilbert space into two subspaces 1 and 2 is an amount of information which can be transmitted through 1 and 2 from a system interacting with 1 to another system interacting with 2. The transmission medium is the quantum entanglement between 1 and 2. In order to support the interpretation, suggestive arguments are given: variational principles in entanglement thermodynamics and quantum teleportation. It is shown that a quantum state having maximal entanglement entropy plays an important role in quantum teleportation. Hence the entanglement entropy is, in some sense, an index of the efficiency of quantum teleportation. Finally, the implications for the information loss problem and Hawking radiation are discussed.
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 Entropy has played an essential role in the history of physics. Its mathematical definition and applications have changed over time till today. In this paper, we first review the historical evolution of these various points of view, from the thermodynamic definition to information entropy from Shannon in classical physics, up to the modern concept of Neumann’s quantum entropy. As a specific example, we consider entanglement entropy and compare the phase space approach in classical physics to the Hilbert space approach in quantum physics in simple model systems. We derive a general expression for the entanglement entropy of fermions and bosons in arbitrary partitions of Hilbert space, valid beyond the thermodynamic limit. Next, we compare thermodynamic heat engines with quantum heat engines. Finally, we proceed to the more general concept of quantum (computational) complexity and argue, using the concept of entanglement entropy, that the Heisenberg time in classically chaotic systems coincides with the time when maximal complexity is reached in the quantum case for systems with all–all interactions.
Entanglement is one of the most useful resources in quantum information processing. If a sender and receiver share noiseless entanglement in the form of maximally entangled states, then Chapter 6 showed how they can teleport quantum bits between each other with the help of classical communication, or they can double the capacity of a noiseless qubit channel for transmitting classical information. We will see further applications in Chapter 20 where they can exploit noiseless entanglement to assist in the transmission of classical or quantum data over a noisy quantum channel. Given the utility of maximal entanglement, a reasonable question is to ask what a sender and receiver can accomplish if they share pure entangled states that are not maximally entangled. In the quantum Shannon-theoretic setting, we make the further assumption that the sender and receiver can share many copies of these pure entangled states. We find out in this chapter that they can “concentrate” these non-maximally entangled states to maximally entangled ebits, and the optimal rate at which they can do so in the asymptotic limit is equal to the “entropy of entanglement” (the von Neumann entropy of half of one copy of the original state). Entanglement concentration is thus another fundamental task in noiseless quantum Shannon theory, and it gives a different operational interpretation to the von Neumann entropy. Entanglement concentration is perhaps complementary to Schumacher compression in the sense that it gives a firm quantum information-theoretic interpretation of the term “ebit” (just as Schumacher compression did for the term “qubit”), and it plays a part in demonstrating how the entropy of entanglement is the unique measure of entanglement for pure bipartite states.
Quantum mechanics and information theory are among the most important scientific discoveries of the last century. Although these two areas initially developed separately, it has emerged that they are in fact intimately related. In this review the author shows how quantum information theory extends traditional information theory by exploring the limits imposed by quantum, rather than classical, mechanics on information storage and transmission. The derivation of many key results differentiates this review from the usual presentation in that they are shown to follow logically from one crucial property of relative entropy. Within the review, optimal bounds on the enhanced speed that quantum computers can achieve over their classical counterparts are outlined using information-theoretic arguments. In addition, important implications of quantum information theory for thermodynamics and quantum measurement are intermittently discussed. A number of simple examples and derivations, including quantum superdense coding, quantum teleportation, and Deutsch's and Grover's algorithms, are also included.
This paper explores the fundamental relationship between the geometry of entanglement and von Neumann entropy, shedding light on the intricate nature of quantum correlations. We provide a comprehensive overview of entanglement, highlighting its crucial role in quantum mechanics. Our focus centers on the connection between entanglement, von Neumann entropy, a measure of the information content within quantum systems and the geometry of composite Hilbert spaces. We discuss various methods for quantifying and characterizing entanglement through a geometric perspective and elucidate how this connection unveils the nature of quantum entanglement, offering valuable insights into the underlying structure of quantum systems. This study underscores the significance of geometry as a key tool for understanding the rich landscape of quantum correlations and their implications across various domains of physics and information theory. An example of entanglement as an indispensable resource for the task of state teleportation is presented at the end.
Entropy plays a pivotal role in quantum computing and information theory, serving as a measure of uncertainty and information in quantum systems. This paper explores how entropy, particularly von Neumann entropy, quantifies quantum states and their evolution in quantum computing systems. We discuss the relationship between entropy and quantum entanglement, quantum error correction, and the thermodynamic properties of quantum computers. Furthermore, we examine the implications of entropy in information processing tasks, including quantum algorithms, and its role in the quantum-to-classical transition.