Perfect quantum information processing with Dicke-class state

We investigate the possibility of implementing perfect quantum information processing with Dicke-class state. It is shown that the symmetric Dicke state |DN(m)〉 only has the maximal bipartite entanglement of one ebit when N = 2m and generally it is not maximally entangled for all bipartitions. By adjusting the suitable weights and relative phases in the Dicke state |DN(m)〉, we present a class of asymmetric Dicke states \(|\overline D_N^{(m)}\rangle\) which have the maximal bipartite entanglement of q (1 ≤ q ≤ m) ebits. We also obtain the sufficient and necessary condition that the Dicke-class states \(|\overline D_{N}^{(m)}\rangle\) have the maximal bipartite entanglement. We illustrate our idea using the four-qubit Dicke state with two excitations. It is shown that our proposed Dicke-class states have distinct advantages over the symmetric Dicke state in perfect quantum information processing.