Generating coherent state 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/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 to N/2 quantum telecloning. We show how the scheme can be implemented in a realistic system of atomic spin qubits in optical lattice. Error analysis show 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 large scale Affleck-Kennedy-Lieb-Tasaki (AKLT) state.Comment: updated version to appear on Phys. Rev.

A note on strong edge-colorings of 2-degenerate graphs

We show that every 2-degenerate graph with maximum degree $\Delta$ has a strong edge-coloring with at most $8\Delta-4$ colors