  We study the new class of solutions in linearized open string field theory
(OSFT) involving higher-spin modes. Unlike the elementary OSFT solutions
(on-shell vertex operators) that, acting on a vacuum, define wavefunctions of
pure states (e.g. a tachyon), the solutions that we describe correspond to the
reduced density matrices which eigenvalues describe the entanglement between
higher-spin modes with different spin values. We compute the entanglement
entropy on these OSFT solutions, and the answer is expressed in terms of
converging series in inverse weighted partition numbers. In the case of
$D$-dimensional bosonic string theory, the entanglement entropy of spin $1$
subsystem and the system of all the spin values is given by
$D{\log{\lambda_0}}+{D\over{\lambda_0}}\sum_{N=3}^\infty{{|\beta(N)|}\over{\lambda(N)}}
{\log{({{\lambda(N)}\over{|\beta(N)|}})}}$, where $\lambda(N)$ is the weighted
number of partitions of $N$,
$\beta(N)={{(N-1)\zeta(3)-\zeta(2)}\over{(N-1)^4}}$ and
$\lambda_0=\sum_{N=1}^{\infty}{{\beta(N)}\over{\lambda(N)}}$ ($\zeta$ is
Riemann's zeta-function). The first term, $D{\log{\lambda_0}}$, represents the
entanglement swapping between string vacuum and string excitations.
  We generalize this result to obtain the entanglement for a subsystem of a
given spin $s$ in a given space-time dimension. We also discuss how open string
field theory may be used to study the entanglement of systems
  other than higher spin excitations in string theory.
