Quantum information: Jaynes and Shannon entropies in a two-electron entangled artificial atom

Dynamics of Entanglement for Two-Electron Atoms

“…For a pure state |Ψ , the von Neumann entropy of the reduced state is a good entanglement measure, 14 although other approaches are possible, for example, Shannon entropy has been used to study the two-electron atom 15,16 and a two-electron artificial atom. 17 The von Neumann entropy has been used to study the dynamics of entanglement between two trapped atoms, 18 the entanglement between two (spin-1/2) fermions in a cylindrical harmonic trap, 19 the entanglement for one-dimensional spin systems in external time-dependent magnetic fields [20][21][22] and the scaling properties of entanglement shared between the two electrons of an atomic like system near the ionization threshold. 23 Gittings and Fisher 24 showed that the von Neumann entropy for the reduced density matrix of half the system can be used as an entanglement measure for the case of indistinguishable particles.…”

Quantum entanglement for two electrons in the excited states of helium-like systems

“…Understanding of entangled systems is important in other research areas such as quantum information [1], quantum computation [2] and quantum cryptography [3]. The investigations of quantum entanglement include the works on some model atoms like the Moshinsky atom [4][5][6][7][8], the Crandall atom [9] and the Hooke atom [9][10][11][12], and the works on artificial atoms like quantum dots [13][14][15][16][17]. Coe and D'Amico calculated the linear entropy for the ground state of the natural helium atom with wave functions constructed by using the products of hydrogenic wave functions, as well as using the density functional theory [10].…”

The von Neumann entanglement entropy for Wigner-crystal states in one dimensional N-particle systems

“…In particular, a few attempts have been made recently towards understanding the entanglement in systems of interacting particles. For example, some light has been shed on entanglement both in quantum dot systems [6][7][8][9][10][11][12][13][14][15] and in systems of harmonically interacting particles in a harmonic trap (the so-called Moshinsky atom) [16][17][18][19][20][21][22][23]. Special attention has also been paid to the study of entanglement in the helium atoms and helium ions [24][25][26][27][28][29][30][31][32].…”