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We propose a scheme to generate a maximally four-dimensional entangled state of two six-level atoms in two remote cavities. By choosing suitable intensities and detunings of fields, atomic spontaneous radiation and photon leakage out of cavity and fibre are efficiently suppressed. Thus, the intended state can be generated with high fidelity in the presence of decoherence. We extend the scheme to generate an N-atom four-dimensional entangled state. [ABSTRACT FROM AUTHOR]

For a tripartite pure state superposed by two individual states, the bipartitely shared entanglement can always be achieved by local measurements of the third party. Consider the different aims of the third party, i.e. maximizing or minimizing the bipartitely shared entanglement, we find bounds on both the possible bipartitely shared entanglement of the superposition state in terms of the corresponding entanglement of the two states being superposed. In particular, by choosing the concurrence as bipartite entanglement measure, we obtain calculable bounds for tripartite (2 ⊗ 2 ⊗ n)-dimensional cases. [ABSTRACT FROM AUTHOR]