Correlation-coupling entropy as a measure of strong electron correlation and fragment-conditional density spin polarization as a measure of electron entanglement

Quantum entanglement has been one of the hottest topics in current day physics, since it is the driving force behind quantum cryptography, quantum teleportation, and quantum computing. Several measures of quantification of entanglement have been proposed, each of which can often only be applied to a few specific systems. In this paper we derive a kinematic measure of entanglement that is capable of giving a full description of Einstein-Podolsky-Rosen entanglement in molecular systems. The associated “coupled entropy” energy contribution generates the correct amount of strong correlation energy for the ${\mathrm{H}}_2$ and ${\mathrm{N}}_2$ prototype systems, and is shown to be able to perform the same feat if it is explicitly used as the correlation component in the density-matrix functional context. And, finally, we propose a nonkinematic way to measure the entanglement of spins by using the conditional density of the system.

Figure 1

Potential-energy curves (6-31G*) for ${\mathrm{H}}_2$ (a), LiH (b), ${\mathrm{H}}_2\mathrm{O}$ (c), and ${\mathrm{N}}_2$ (d). The ${\mathrm{H}}_2\mathrm{O}$ equilibrium geometry is slightly distorted in order to break the symmetry. Only a single O-H bond is broken for the ${\mathrm{H}}_2\mathrm{O}$ molecule.