Related papers: Von Neumann entropy from unitarity
Entropy is one of the most basic concepts in thermodynamics and statistical mechanics. The most widely used definition of statistical mechanical entropy for a quantum system is introduced by von Neumann. While in classical systems, the…
The von Neumann entropy of an $n$-partite system $A_1^n$ given a system $B$ can be written as the sum of the von Neumann entropies of the individual subsystems $A_k$ given $A_1^{k-1}$ and $B$. While it is known that such a chain rule does…
We review the postulates of quantum mechanics that are needed to discuss the von Neumann's entropy. We introduce it as a generalization of Shannon's entropy and propose a simple game that makes easier understanding its physical meaning.
The insertion of a magnetic impurity in a superconductor induces a first order quantum phase transition as the coupling to the electronic spin density increases. As the transition is crossed, a discontinuity is exhibited by various…
Let S be the von Neumann entropy of a finite ensemble E of pure quantum states. We show that S may be naturally viewed as a function of a set of geometrical volumes in Hilbert space defined by the states and that S is monotonically…
This paper investigates the relationship between categorical entropy and von Neumann entropy of quantum lattices. We begin by studying the von Neumann entropy, proving that the average von Neumann entropy per site converges to the logarithm…
We study the quantum entanglement caused by unitary operators that have classical limits that can range from the near integrable to the completely chaotic. Entanglement in the eigenstates and time-evolving arbitrary states is studied…
By carrying out appropriate continuous quantum measurements with a family of projection operators, a unitary channel can be approximated in an arbitrary precision in the trace norm sense. In particular, the quantum Zeno effect is described…
The change of the von Neumann entropy of a set of harmonic oscillators initially in thermal equilibrium and interacting linearly with an externally driven quantum system is computed by adapting the Feynman-Vernon influence functional…
The Bures-Hall distance metric between quantum states is a unique measure that satisfies various useful properties for quantum information processing. In this work, we study the statistical behavior of quantum entanglement over the…
In this paper, we characterize the saturation of four universal inequalities in quantum information theory, including a variant version of strong subadditivity inequality for von Neumann entropy, the coherent information inequality, the…
Von Neumann entropy (VNE) is a fundamental quantity in quantum information theory and has recently been adopted in machine learning as a spectral measure of diversity for kernel matrices and kernel covariance operators. While maximizing VNE…
With the help of von Neumann entropy, we study numerically the localization properties of two interacting particles (TIP) with on-site interactions in one-dimensional disordered, quasiperiodic, and slowly varying potential systems,…
A renormalized version of the von Neumann quantum entropy (which is finite and continuous in general, infinite dimensional case) and which obeys several of the natural physical demands (as expected for a "good" measure of entanglement in…
Environmental interactions are ubiquitous in any real-world application of a quantum information processing protocol. Such interactions result in depletion of quantum resources. Two important figure of merits in the context of quantum…
We extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (``universal probability'') as a starting point, and define complexity (an operator) as its negative logarithm. A number of…
In quantum systems with infinitely many degrees of freedom, states can be infinitely entangled across a pair of subsystems, but are there different forms of infinite entanglement? To understand entanglement in such systems, we use a…
Entanglement is the defining characteristic of quantum mechanics. Bipartite entanglement is characterized by the von Neumann entropy. Entanglement is not just described by a number, however; it is also characterized by its level of…
The mathematical structure of quantum entanglement is studied and classified from the point of view of quantum compound states. We show that t he classical-quantum correspondences such as encodings can be treated as dia gonal (d-)…
The deep connection between entropy and information is discussed in terms of both classical and quantum physics. The mechanism of information transfer between systems via entanglement is explored in the context of decoherence theory. The…