Entangling qubit registers via many-body states of ultracold atoms

Inspired by the experimental measurement of the Rényi entanglement entropy in a lattice of ultracold atoms by Islam et al. [Nature (London) 528, 77 (2015)], we propose a method to entangle two spatially separated qubits using the quantum many-body state as a resource. Through local operations accessible in an experiment, entanglement is transferred to a qubit register from atoms at the ends of a one-dimensional chain. We compute the operational entanglement, which bounds the entanglement physically transferable from the many-body resource to the register, and discuss a protocol for its experimental measurement. Finally, we explore measures for the amount of entanglement available in the register after transfer, suitable for use in quantum information applications.

Figure 1

Schematic setup whereby entanglement can be transferred from a quantum many-body state $|\mathrm{\Psi }\rangle$ to a quantum register composed of two spatially separated qubits (Bloch spheres).

Figure 2

Spatial second Rényi entropy $S_2$ and operational entanglement $S_2^{\mathrm{op}}$ for symmetric bipartitions $\ell =L/2$ of the Bose-Hubbard model. Curves increase in saturation for $L=N=6,8,10,12$. The dashed vertical line indicates the location of the thermodynamic phase transition.

Figure 3

Shown on the top left is an array of 20 optical lattice sites forming the two copies necessary to measure the second Rényi entropy. The remaining panels show the protocol (described in the text) to transfer entanglement from a many-body state in $A\cup B\cup C$ to spatially separated qubits $Q_A$ and $Q_B$. Solid lines correspond to a large tunnel barrier, double arrows represent the application of a swap operation, and single arrows indicate performing many-body interference.

Figure 4

Logarithmic negativity $E_{\mathcal{N}}$, entanglement of formation $E_F$, and two-copy Rényi mutual information $I_2\left(AB\right)$ of the spatially separated qubits obtained from the $L=N=6$ Bose-Hubbard ground state. The inset shows the probability of projecting onto a state with a single particle in each of $A$ and $B$. The dashed vertical line indicates the location of the thermodynamic phase transition.