Linear entropy as an entanglement measure in two-fermion systems

Abstract

We describe an efficient theoretical criterion, suitable for indistinguishable particles to quantify the quantum correlations of any pure two-fermion state, based on the Slater rank concept. It represents the natural generalization of the linear entropy used to treat quantum entanglement in systems of non-identical particles. Such a criterion is here applied to an electron-electron scattering in a two-dimensional system in order to perform a quantitative evaluation of the entanglement dynamics for various spin configurations and to compare the linear entropy with alternative approaches. Our numerical results show the dependence of the entanglement evolution upon the initial state of the system and its spin components. The differences with previous analyses accomplished by using the von Neumann entropy are discussed.The evaluation of the entanglement dynamics in terms of the linear entropy results to be much less demanding from the computational point of view, not requiring the diagonalization of the density matrix.

Ground-State Entanglement Properties of Helium Atom in a Finite Spherical Cavity

“…Deviations from such a form is used to measure the amount of entanglement in the system. The wellknown entanglement measures are the von Neumann (vN) entropy [26] or its approximation the so-called a linear entropy [27]. Here we are only interested in S-symmetry ground-state, the spatial wavefunction of which depends explicitly only on the radial coordinates r 1 , r 2 and the inter-electronic angle coordinate θ , ψ(r 1 , r 2 ) ≡ ψ(r 1 , r 2 , cos θ).…”

Magnetic alteration of entanglement in two-electron quantum dots

“…For instance, a two-fermion state of a Slater rank 1 (i.e., a state represented by one Slater determinant) must be regarded as non-entangled, and its measure has to be zero. In order to satisfy this requirement, the entanglement measure based on the linear entropy in the case of two identical fermions has the form (see, for example, [14,15,23])…”

“…Besides computational problems for many-body quantum systems, one has to address to the problem of measuring entanglement for indistinguishable particles. In other words, one has to discriminate entanglement from correlations due to the statistics of indistinguishable particles [13][14][15]. In spite of this difficulty, bipartite entanglement has been investigated in a number of systems of physical interest with the aid of various numerical approaches at zero magnetic field.…”

Entropic entanglement criteria for Fermion systems

“…Entanglement in fermion systems has been studied in connection with different problems, such as the entanglement between electrons in a conducting band [7], the entanglement dynamics associated with scattering processes involving two electrons [8], the role played by entanglement in the time-optimal evolution of fermionic systems [9,10], the classification of three fermion states based on their entanglement features [11], the detection of entanglement in fermion systems through the violation of appropriate uncertainty relations [12], the entanglement features of fractional quantum Hall liquids [13] and the entanglement properties of the eigenstates of soluble two-electrons atomic models [14].…”