Quantum entanglement is an important resource in quantum information processing. Estimation of quantum entanglement for general mixed states is a challenging problem. We introduce the concept of a “cooperative local unitary (co-LU) set” and provide specific constructions of such co-LU sets for bipartite systems. These co-LU sets give rise to analytical formulas of entanglement for classes of quantum mixed states under any entanglement measures. Detailed examples are given to illustrate the calculation of entanglement for a class of mixed states in terms of the informationally complete entanglement measure, concurrence and $q$-concurrence, showing the superiority of our analytical results to the ones from the lower bounds of these measures. Our approach simplifies the estimation on entanglement for classes of quantum states and provides a new perspective for understanding the entanglement.

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• Quantum correlations in quantum information
• Quantum entanglement