Generating coherent states of entangled spins

A coherent state of many spins contains quantum entanglement, which increases with a decrease in the collective spin value. We present a scheme to engineer this class of pure state based on incoherent spin pumping with a few collective raising or lowering operators. In a pumping scenario aimed for maximum entanglement, the steady state of N-pumped spin qubits realizes the ideal resource for the 1→(N)/(2) quantum telecloning. We show how the scheme can be implemented in a realistic system of atomic spin qubits in an optical lattice. Error analysis shows that high-fidelity state engineering is possible for N∼O(100) spins in the presence of decoherence. The scheme can also prepare a resource state for the secret sharing protocol and for the construction of the large-scale Affleck-Kennedy-Lieb-Tasaki state.