Related papers: A study of two-qubit density matrices with fermion…
We consider the problems of maximizing the entanglement negativity of X-form qubit-qutrit density matrices with (i) a fixed spectrum and (ii) a fixed purity. In the first case, the problem is solved in full generality whereas, in the…
In the spirit of the generalized one-particle density matrix for fermions, we introduce generalized one- and two-particle density matrices to state representability conditions up to second order for boson systems without assuming particle…
This paper is a continuation of our previous paper [8], in which we have studied the dynamics of quantum correlations of two qubits embedded each into its own disordered multiconnected environment. We modeled the environment by random…
Entanglement criteria for general (pure or mixed) states of systems consisting of two identical fermions are introduced. These criteria are based on appropriate inequalities involving the entropy of the global density matrix describing the…
We develop a comprehensive model for the effective two-photon density matrix produced by a parametric source of entangled photon pairs under a variety of detector configurations commonly seen in a laboratory setting: two and four photon…
The methods of quantum chemistry and solid state theory to solve the many-body problem are reviewed. We start with the definitions of reduced density matrices, their properties (contraction sum rules, spectral resolutions, cumulant…
Statistical properties of ensembles of random density matrices are investigated. We compute traces and von Neumann entropies averaged over ensembles of random density matrices distributed according to the Bures measure. The eigenvalues of…
Relying on the mathematical analogy of the pure states of a two-qubit system with four-component Dirac spinors, we provide an alternative consideration of quantum entanglement using the mathematical formulation of Cartan's pure spinors. A…
Eigenvalues of a density matrix characterize well the quantum state's properties, such as coherence and entanglement. We propose a simple method to determine all the eigenvalues of an unknown density matrix of a finite-dimensional system in…
Entanglement concurrence is an important bipartite entanglement measure that has found wide applications in quantum technologies. In this work, inspired by unified entropy, we introduce a two-parameter family of entanglement measures,…
Defining, in the framework of quantum field theory, their mass eigenstates through their matricial propagator, we show why the mixing matrices of non-degenerate coupled systems should not be parametrized as unitary. This is how, for…
The nonlinear positive map of density matrix of two-qubit Werner state called nonlinear channel is studied. The map of density matrix is realized by rational function. The influence of the map onto the entanglement properties of the…
A new density matrix and corresponding quantum kinetic equations are introduced for fermions undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection). A central element in our derivation…
Recently, it has been shown, that the pair density of the homogeneous electron gas can be parametrized in terms of 2-body wave functions (geminals), which are scattering solutions of an effective 2-body Schr\"odinger equation. For the…
We review recently introduced numerical methods for the unbiased detection of the order parameter and/or dominant correlations, in many-body interacting systems, by using reduced density matrices. Most of the paper is devoted to the…
Quantities invariant under local unitary transformations are of natural interest in the study of entanglement. This paper deduces and studies a particularly simple quantity that is constructed from a combination of two standard permutations…
A method allowing to increase a computational efficiency of evaluation of non-local characteristics of a pair of qubits is described. The method is based on the construction of coordinates on a generic section of 2-qubit's entanglement…
We study the normal form of multipartite density matrices. It is shown that the correlation matrix (CM) separability criterion can be improved from the normal form we obtained under filtering transformations. Based on CM criterion the…
In this paper we study the state determination for composite systems of two spatial qubits. We show, theoretically, that one can use the technique of quantum tomography to reconstruct the density matrixes of these systems. This tomographic…
We discuss the ground state and the small-amplitude excitations of a degenerate vapour of fermionic atoms placed in two hyperfine states inside a spherical harmonic trap. An equations-of-motion approach is set up to discuss the hydrodynamic…