  Entanglement concurrence has been widely used for featuring entanglement in
quantum experiments. As an entanglement monotone it is related to specific
quantum Tsallis entropy. Our goal in this paper is to propose a new
parameterized bipartite entanglement monotone which is named as $q$-concurrence
inspired by general Tsallis entropy. We derive an analytical lower bound for
the $q$-concurrence of any bipartite quantum entanglement state by employing
positive partial transposition criterion and realignment criterion, which shows
an interesting relationship to the strong separability criteria. The new
entanglement monotone is used to characterize bipartite isotropic states.
Finally, we provide a computational method to estimate the $q$-concurrence for
any entanglement by superposing two bipartite pure states. It shows that the
superposition operations can at most increase one ebit for the $q$-concurrence
in the case that the two states being superposed are bi-orthogonal or one-sided
orthogonal. These results reveal a series of new phenomena about the
entanglement, which may be interesting in quantum communication and quantum
information processing.
