  Presence of entangled states is explicitly shown in Topological insulator
(TI) $Bi_2Te_3$. The surface and bulk state are found to have the different
structures of entanglement. The surface states live as maximally entangled
states in the four-dimensional subspace of total Hilbert space (spin, orbital,
space). However, bulk states are entangled in the whole Hilbert space. Bulk
states are found to be entangled maximally by controlled injection of electrons
with momentum only along the z-direction. Scheme to detect entanglement in a
2-D model using measurement, confirming natural implementation of universal
Hadamard with Controlled-NOT gates is explicated.
