The evolution of $N$ spin-$1/2$ system with long-range Ising-type interaction
is considered. For this system we study the entanglement of one spin with the
rest spins. It is shown that the entanglement depends on the amount of spins
and the initial state. Also the geometry of manifold which contains entangled
states is obtained. Finally we find the dependence of entanglement on the
scalar curvature of manifold and examine it for different number of spins in
the system.

We propose a formal resource theoretic approach to quantify the degree of
polarization of two and three-dimensional random electromagnetic fields. We
show that this path provides a comprehensive framework to tackle the problem
and that, endowing the space of spectral polarization matrices with the orders
induced by majorization or convex mixing, one naturally recovers the best known
polarization measures.

Statistical mechanics is founded on the assumption that a system can reach
thermal equilibrium, regardless of the starting state. Interactions between
particles facilitate thermalization, but, can interacting systems always
equilibrate regardless of parameter values\,? The energy spectrum of a system
can answer this question and reveal the nature of the underlying phases.
However, most experimental techniques only indirectly probe the many-body
energy spectrum. Using a chain of nine superconducting qubits, we implement a

The semileptonic decay asymmetry $\mathcal{A}_{\Delta m}$ is studied within
the open quantum systems approach to the physics of the neutral meson
$B^0$-$\overline{B^0}$ system: this extended treatment takes into account
possible non-standard, dissipative effects induced by the presence of an
external environment. A bound on these effects is provided through the analysis
of available experimental data from the Belle Collaboration.

We address the dynamics of a bosonic system coupled to either a bosonic or a
magnetic environment, and derive a set of sufficient conditions that allow one
to describe the dynamics in terms of the effective interaction with a classical
fluctuating field. We find that for short interaction times the dynamics of the
open system is described by a Gaussian noise map for several different
interaction models and independently on the temperature of the environment. In

Quantum criticality usually occurs in many-body systems. Recently it was
shown that the quantum Rabi model, which describes a two-level atom coupled to
a single model cavity field, presents quantum phase transitions from a normal
phase to a superradiate phase when the ratio between the frequency of the two
level atom and the frequency of the cavity field extends to infinity. In this
work, we study quantum phase transitions in the quantum Rabi model from the

High-dimensional encoding of quantum information provides a promising method
of transcending current limitations in quantum communication. One of the
central challenges in the pursuit of such an approach is the certification of
high-dimensional entanglement. In particular, it is desirable to do so without
resorting to inefficient full state tomography. Here, we show how carefully
constructed measurements in two or more bases can be used to efficiently
certify high-dimensional states and their entanglement under realistic

Topological insulators and superconductors at finite temperature can be
characterised by the topological Uhlmann phase. However, a direct experimental
measurement of this invariant has remained elusive in condensed matter systems.
Here, we report a measurement of the topological Uhlmann phase for a
topological insulator simulated by a system of entangled qubits in a
superconducting qubit platform. By making use of ancilla states, otherwise
unobservable phases carrying topological information about the system become

The Hohenberg-Kohn theorem plays a fundamental role in density functional
theory, which has become a basic tool for the study of electronic structure of
matter. In this article, we study the Hohenberg-Kohn theorem for a class of
external potentials based on a unique continuation principle.

Many equations have been introduced and derived by the author indicated in
the title in relation to multi-electron densities between the Hohenberg-Kohn
theorems and variational principle, conversion of the non-relativistic
electronic Schrodinger equation to scaling correct moment functional of ground
state one-electron density to estimate ground state electronic energy,
participation of electron-electron repulsion energy operator in the
non-relativistic electronic Schrodinger equation via the coupling strength