Entanglement for a two-parameter class of states in $2\otimes n$ quantum system

Abstract

We exhibit a two-parameter class of states $\rho_{(\alpha,\gamma)}$, in $2\otimes n$ quantum system for $n\ge 3$, which can be obtained from an arbitrary state by means of local quantum operations and classical communication, and which are invariant under all bilateral %unitary operations %of the form $U\otimes U$ on $2\otimes n$ quantum system. We calculate the negativity of $\rho_{(\alpha,\gamma)}$, and a lower bound and a tight upper bound on its entanglement of formation. It follows from this calculation that the entanglement of formation of $\rho_{(\alpha,\gamma)}$ cannot exceed its negativity.