Related papers: Average relative entropy of random states
It was recently conjectured by D. Page that if a quantum system of Hilbert space dimension $nm$ is in a random pure state then the average entropy of a subsystem of dimension $m$ where $m \leq n$ is $ S_{mn} = \sum^{mn}_{k=n+1}(1/k) -…
So-called average subsystem entropies are defined by first taking partial traces over some pure state to define density matrices, then calculating the subsystem entropies, and finally averaging over the pure states to define the average…
Quantum relative entropy, a quantum generalization of the renowned Kullback-Leibler divergence, serves as a fundamental measure of the distinguishability between quantum states and plays a pivotal role in quantum information science.…
The relative entropy between quantum states quantifies their distinguishability. The estimation of certain relative entropies has been investigated in the literature, e.g., the von Neumann relative entropy and sandwiched R\'enyi relative…
Relative entropy serves as a fundamental measure of state distinguishability in both quantum information theory and relativistic quantum field theory. Despite its conceptual importance, however, explicit computations of relative entropy…
The density matrix formalism is a fundamental tool in studying various problems in quantum information processing. In the space of density matrices, the most well-known measures are the Hilbert-Schmidt and Bures-Hall ensembles. In this…
An universal approximation technique for analysis of different characteristics of states of composite infinite-dimensional quantum systems is proposed and used to prove general results concerning the properties of correlation and…
An essential quantity in quantum information theory is the von Neumann entropy which depends entirely on the quantum density operator. Once known, the density operator reveals the statistics of observables in a quantum process, and the…
The fermionic relative entropy in two-dimensional Rindler spacetime is studied using both modular theory and the reduced one-particle density operators. The methods and results are compared. A formula for the relative entropy for general…
We compute Araki's relative entropy associated to a bounded interval $I=(a,b)$ between a thermal state and a coherent excitation of itself in the bosonic U(1)-current model, namely the (derivative of the) chiral boson. For this purpose we…
We define correlational (von Neumann) entropy for an individual quantum state of a system whose time-independent hamiltonian contains random parameters and is treated as a member of a statistical ensemble. This entropy is representation…
We study the Hilbert-Schmidt measure on the manifold of mixed Gaussian states in multi mode continuous variable quantum systems. An analytical expression for the Hilbert-Schmidt volume element is derived. Its corresponding probability…
This dissertation investigates relative entropies, also called generalized divergences, and how they can be used to characterize information-theoretic tasks in quantum information theory. The main goal is to further refine characterizations…
We introduce variants of relative entropy of entanglement based on the optimal distinguishability from unentangled states by means of restricted measurements. In this way, we are able to prove that the standard regularized entropy of…
In the last decades, it has been understood that a wide variety of phenomena in quantum field theory (QFT) can be characterised using quantum information measures, such as the entanglement entropy of a state and the relative entropy between…
Our capacity to process information depends on the computational power at our disposal. Information theory captures our ability to distinguish states or communicate messages when it is unconstrained with unrivaled beauty and elegance. For…
Various properties of relative entropy have led to its widespread use in information theory. These properties suggest that relative entropy has a role to play in systems that attempt to perform inference in terms of probability…
The quantum relative entropy is known to play a key role in determining the asymptotic convertibility of quantum states in general resource-theoretic settings, often constituting the unique monotone that is relevant in the asymptotic…
Quantum entanglement plays a crucial role in quantum information, quantum teleportation and quantum computation. The information about the entanglement content between subsystems of the composite system is encoded in the Schmidt…
The asymptotic equipartition property (AEP) states that in the limit of a large number of independent and identically distributed (i.i.d.) random experiments, the output sequence is virtually certain to come from the typical set, each…