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

In the context of quantum information, both Shannon entropy and the different Jaynes entropy for a two-electron “entangled artificial” atom proposed by Moshinsky are studied here. The Jaynes entropy in this model is shown to be intimately related to the correlation kinetic energy. A generalization of the customary Shannon entropy based on the electron density is then proposed in terms of the electron pair correlation function. Both definitions behave in a similar way to the Jaynes entropy when considered as a function of the strength of the model electron-electron interaction.

Figure 1

Correlation kinetic energy contributions $T_W^{\left(\mathit{corr}\right)}$ (lower curve) and $6B$ (upper curve) of Eq. (11) against the interparticle spring constant $K$. Data are in atomic units.

Figure 2

Plot of Shannon entropy defined in Eq. (12) got from Hartree-Fock density against the interparticle spring constant $K$. Data are in atomic units.

Figure 3

Plot of Jaynes entropy $\left(J\right)$ and of correlation Shannon entropies ($S1$ and $S2$) defined in Eq. (16) against the interparticle spring constant $K$. Data are in atomic units.

Figure 4

Plot of the correlation kinetic energy against Jaynes entropy. Data are in atomic units.