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We find that the mixed maximally entangled states exist and prove that the form of the mixed maximally entangled states is unique in terms of the entanglement of formation. Moreover, even if the entanglement is quantified by other entanglement measures, this conclusion is still proven right. This result is a supplementary to the generally accepted fact that all maximally entangled states are pure. These states possess important properties of the pure maximally entangled states, for example, these states can be used as a resource for faithful teleportation and they can be distinguished perfectly by local operations and classical communication., 7 pages

We explore how entanglement of a general bipartite system evolves when one subsystem undergoes the action of an arbitrary noisy channel. It is found that the dynamics of entanglement for general bipartite systems under the influence of such channel is determined by the channel's action on the maximally entangled state, which includes as a special case the results for two-qubit systems [Nature Physics 4, 99 (2008)]. In particular, for multi-qubit or qubit-qudit systems, we get a general factorization law for evolution equation of entanglement with one qubit being subject to a noisy channel. Our results can help the experimental characterization of entanglement dynamics., 4 pages, 1 figure