LDA Entanglement in two-electron systems

Entanglement, which is one of the stranger features of quantum mechanics, is now seen as a
resource that can be exploited for teleportation of quantum states and secure
distribution of cryptographic keys. In addition, it is thought of as one of the
main reasons that quantum information devices may be able to outperform their
classical counterparts. In this respect, many solid state systems have merit as
quantum information processors, for example, quantum dots. However, exactly
modeling solid state many-body systems is often computationally intractable;
hence, approximations are used. We present methods of calculating the spatial
entanglement of an interacting electron system within the framework of
density-functional theory [1]. These methods are tested on a model quantum dot
system (3-dimensional Hooke\'s atom) and on one-dimensional systems with tailored
densities [2]. We analyze how the strength of the confining potential affects the
spatial entanglement and how accurately the methods that we introduced reproduce
the exact trends.

[1] J.P. Coe, A. Sudbery and I. D\'Amico, Phys. Rev. B 77, 205122 (2008)
[2] J. P. Coe, I. D\'Amico, arXiv:0905.4645