Exploiting quench dynamics in spin chains for distant entanglement and quantum communication

We suggest a method of entangling significantly the distant ends of a spin chain using minimal control. This entanglement between distant individual spins is brought about solely by exploiting the dynamics of an initial mixed state with Néel order if the lattice features nearest-neighbor $XXZ$ interaction. There is no need to control single spins or to have engineered couplings or to pulse globally. The method only requires an initial nonadiabatic switch (a quench) between two Hamiltonians followed by an evolution under the second Hamiltonian. The scheme is robust to randomness of the couplings as well as the finiteness of an appropriate quench and could potentially be implemented in various experimental setups, ranging from atoms in optical lattices to Josephson-junction arrays.

Figure 1

(Color online) Schematic of our proposal of entangling distant spins. Alice and Bob are at opposite ends of the chain. First, the spin chain is initialized in the antiferromagnetic Ising ground state. By a nonadiabatic switching to an $XY$ interaction and subsequent time-evolution quantum correlations (entanglement) is being established between Alice’s and Bob’s spins.

Figure 2

Fully entangled fraction $f$ evaluated at time $t=T_{\text{max}}$ as a function of system size $N$ in a semilogarithmic scale. The data points for the analytic quench scenario (circles) exceed 0.5 for chains up to $N=241$ spins. We find a good agreement of these data for $N\ge 25$ to a function of the form $g^{\text{fit}}\left(N\right)\propto 1.42\left(9\right)N^{-\nu }$ with $\nu =0.22\left(9\right)$ (dashed curve). For $N\le 11$, the figure is supplemented with data from numerical diagonalization for more general quench characteristics $\left({\Delta }_1\to {\Delta }_2\right)$: $\left(\infty \to 1\right)$ (triangles) and $\left(3\to 0\right)$ (squares). Left inset: typical time evolution of $f$ in a quench $\left(\infty \to 0\right)$ for $N=7$ with first maximum at $T_{\text{max}}$ (vertical line). Disorder ($\delta =0,0.1,0.2,0.3$ from top to bottom curves, respectively) is seen not to affect the amount of entanglement seriously and leaves $T_{\text{max}}$ almost unchanged (average taken over 100 realizations). Right inset: linear scaling of $T_{\text{max}}$ with $N$.