Useful entanglement from the Pauli principle

We address the question whether identical-particle entanglement is a useful resource for quantum information processing. We answer this question positively by reporting a scheme to create entanglement using semiconductor quantum wells. The Pauli exclusion principle forces quantum correlations between the spins of two independent fermions in the conduction band. Selective electron-hole recombination then transfers this entanglement to the polarization of emitted photons, which can subsequently be used for quantum information tasks.

Figure 1

(Color online) (a) Band structure for the semiconductor quantum well. For each value of $k$, there can exist just two electrons according to the Pauli principle. (b) Selection rules force the transitions $J_z=-\frac{3}{2}\leftrightarrow J_z=-\frac{1}{2}$ through an emission or absorption of a ${\sigma }_{+}$ photon and $J_z=\frac{3}{2}\leftrightarrow J_z=\frac{1}{2}$ through an emission or absorption of a ${\sigma }_{-}$ photon.

Figure 2

(Color online) Photonic entanglement versus $d=\mid k-k^{\prime }\mid$. Green dotted line, $\delta =2$; black solid line, $\delta =4$; red dashed curve, $\delta =6$, where $\delta$ is a measure of the width of the momentum distribution, assumed the same for electrons and holes [see Eq. (12)]. We see that the greater the spread in the momentum, the higher the entanglement between the photons. This is due to the fact that wider momentum distributions blur the difference in $k$’s, so that once again, it is impossible to distinguish the electrons by momentum.