Related papers: Understanding von Neumann's entropy
Extending black-hole entropy to ordinary objects, we propose kinetic entropy tensor, based on which a quantum gravity tensor equation is established. Our investigation results indicate that if N=1, the quantum gravity tensor equation…
Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and, as well as being fundamental to our understanding of quantum theory, they have practical applications such as for…
We develop the argument that the Gibbs-von Neumann entropy is the appropriate statistical mechanical generalisation of the thermodynamic entropy, for macroscopic and microscopic systems, whether in thermal equilibrium or not, as a…
We formulate and prove a quantum Shannon-McMillan theorem. The theorem demonstrates the significance of the von Neumann entropy for translation invariant ergodic quantum spin systems on n-dimensional lattices: the entropy gives the…
The von Neumann entanglement entropy is a useful measure to characterize a quantum phase transition. We investigate the non-analyticity of this entropy at disorder-dominated quantum phase transitions in non-interacting electronic systems.…
The entropic uncertainty principle in the form proven by Maassen and Uffink yields a fundamental inequality that is prominently used in many places all over the field of quantum information theory. In this work, we provide a family of…
Classical and quantum information theory are simply explained. To be more specific it is clarified why Shannon entropy is used as measure of classical information and after a brief review of quantum mechanics it is possible to demonstrate…
Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a…
A formulation of quantum mechanics, which begins by postulating assertions for individual physical systems, is given. The statistical predictions of quantum mechanics for infinite ensembles are then derived from its assertions for…
We derive a universal inequality that provides a lower bound on the ensemble-averaged von Neumann entropy change in a quantum system subject to continuous measurement and dissipation. Our result clarifies how entropy production is…
By formulating the axioms of quantum mechanics, von Neumann also laid the foundations of a "quantum probability theory". As such, it is regarded a generalization of the "classical probability theory" due to Kolmogorov. Outside of quantum…
We compare the thermodynamic entropy of a quantum Brownian oscillator derived from the partition function of the subsystem with the von Neumann entropy of its reduced density matrix. At low temperatures we find deviations between these two…
We provide an introduction to the theory of quantum measurements that is centered on the pivotal role played by John von Neumann's model. This introduction is accessible to students and researchers from outside the field of foundations of…
Monotonicity under coarse-graining is a crucial property of the quantum relative entropy. The aim of this paper is to investigate the condition of equality in the monotonicity theorem and in its consequences such as the strong…
R\'enyi entropy is a one-parameter generalization of Shannon entropy, which has been used in various fields of physics. Despite its wide applicability, the physical interpretations of the R\'enyi entropy are not widely known. In this paper,…
Entropy is a fundamental concept in equilibrium statistical mechanics, yet its origin in the non-equilibrium dynamics of isolated quantum systems is not fully understood. A strong consensus is emerging around the idea that the stationary…
An elementary formula for the von Neumann and Renyi entropies describing quantum correlations in two-fermionic systems having four single particle states is presented. An interesting geometric structure of fermionic entanglement is…
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…
Entropic measures provide analytic tools to help us understand correlation in quantum systems. In our previous work, we calculated linear entropy and von Neumann entropy as entanglement measures for the ground state and lower lying excited…
We propose a generalization of the quantum entropy introduced by Wigner and von Neumann in 1929 [Zeitschrift f\"ur Physik 57, 30 (1929)]. Our generalization is applicable to both quantum pure states and mixed states. When the dimension $N$…