to an arbitrary state of two spin halves. On the other hand, the entanglements in mixed-spin or higher spin systems are not well-studied due to the lack of good operational entanglement measures. There are several initial studies along this direction [@Schliemann; @Yi; @Zhu], however these works are restricted to the case of two particles.

For the case of higher spins, a non-entangled state has necessarily a positive partial transpose according to the Peres-Horodecki criterion [@PH]. In the case of two spin halves, and the case of (1/2,1) mixed spins, fortunately, a positive partial transpose is also sufficient. Thus, the sufficient and necessary condition for entangled state in (1/2,1) mixed spin systems is that it has a negative partial transpose. This allows us to investigate entanglement features of the mixed spin system.

The Peres-Horodecki criterion give a qualitative way for judging whether the state is entangled or not. The quantitative version of the criterion was developed by Vidal and Werner [@Vidal]. They presented a measure of entanglement called negativity that can be computed efficiently, and the negativity does not increase under local manipulations of the system. The negativity of a state $\rho$ is defined as $${\cal N(\rho)}=\sum_i|\mu_i|,$$ where $\mu_i$ is the 