Entanglement generation via a completely mixed nuclear spin bath

We show that qubits coupled sequentially to a mesoscopic static completely mixed spin bath via the Heisenberg interaction can become highly entangled. Straightforward protocols for the generation of multipartite entangled Greenberger-Horne-Zeilinger (GHZ) states are presented. We show the feasibility of an experimental realization in a quantum dot by the hyperfine interaction of an electron with the nuclear spins.

Figure 1

(Color online) Left: Sketch of the protocol. (a) The $z$-polarized “control electron” interacts resonantly with the nuclear spin bath. (b) A sequence of $x$-polarized electrons interacts off-resonantly with the bath. (c) The control electron interacts resonantly again and is then measured in the $z$ basis. Right: Time dependence of overlap $F$ with Bell state $|{\varphi }_{-}⟩=\left(|++⟩-|--⟩\right)/\sqrt{2}$ (solid blue line) for $N={10}^3$. The dashed red line shows the probability $P$ for a $\downarrow$ measurement.