In the present communication we explore and develop the theory of entanglement measures. As a result we obtain a general criterion of a bipartite mixed states entanglement due to the quasi‐mutual entropy for a single trapped two‐level ion interacting with a laser field. This general expression of the entanglement degree is obtained with the physical significance and without the diagonal approximation. We indicate how the entanglement affected by different values of the Lamb‐Dicke parameter of the initially generalized binomial state. Among the new features found, it is shown, for the large number of quanta, that the shape of entanglement could oscillate around the maximum value, which is related to the existence of a strong entanglement in the present system. (© 2004 by HMS Consultants. Inc. Published exclusively by WILEY‐VCH Verlag GmbH & Co.KGaA)