Concepts Review, Density Matrix, and Entanglement Entropy

Hiu Yung Wong

Sibel Başkal, Marilyn E. Noz

In this review article, we first introduce the density matrix, along with its properties and time evolution. We note that one of the principal uses of the density matrix is to calculate measurement probabilities in quantum mechanics. When only some of the variables can be measured, it is necessary to integrate out the variables that are inaccessible to measurement. The resulting subsystem is then analogous to an open quantum system, where the unmeasured variables belong to an unspecified environment. Coupled and Lorentz-covariant harmonic oscillators are described and their differences are explained. We introduce the density matrix for two harmonic oscillators and demonstrate how they become entangled as well as entangled excited states of the Lorentz-covariant harmonic oscillator. We elaborate on the concept of von Neumann entropy and show how entropy increases when not all the variables of the system can be measured. We use the timeseparation between quarks as an example of an unmeasurable quantity and then present a discussion of von Neumann entropy and entanglement. We include “boiling quarksgluons”, whose most interesting feature is the transition from the confinement phase to the plasma phase, to illustrate the application of the density function and entropy. In this context, we discuss the quark-parton puzzle and a possible explanation.

Manuela Kulaxizi

Said Elakhal, Moulay Brahim Sedra

This paper presents a systematic review (SLR) of quantum entanglement for black holes (BH). The review utilizes databases such as Scopus, Science Direct, and Web of Science to find 250 requested texts. Through the PRISMA protocol, we found 91 papers to be analyzed with NVIVO and VOSviewer. After analyzing the corpus, we found that the most important topics are as follows. Black holes, entanglement entropy, quantum field theory, entanglement of the subsystem, S-matrix, density matrix, string theory, quantize the Hamiltonian, and quantum gravity... The most important methodology used by the authors is also modeling methodology, geometry, topology, and replica trick. The co-occurrence and co-authorship analyses provided insights into the collaborative nature of this research field and the interconnectedness of various concepts. The analysis revealed significant trends and patterns in the literature, including the prevalence of certain journals and the evolution of research over time.

Dominik Janzing