  We calculate the entanglement and the universal boundary entropy (BE) in the
critical quantum spin chains, such as the transverse field Ising chain and the
XXZ chain, with arbitrary direction of the boundary magnetic field (ADBMF). We
determine the boundary universality class that an ADBMF induces. In particular,
we show that the induced boundary conformal field theory (BCFT) depends on the
point on the Bloch sphere where the boundary magnetic field directs. We show
that the classification of the directions boils down to the simple fact that
the boundary field breaks the bulk symmetry or does not. We present a procedure
to estimate the universal BE, based on the finite-size corrections of the
entanglement entropy, that apply to the ADBMF. To calculate the universal BE in
the XXZ chain, we use the density matrix renormalization group (DMRG). The
transverse field XY chain with ADBMF after Jordan-Wigner (JW) transformation is
not a quadratic free fermion Hamiltonian. We map this model to a quadratic free
fermion chain by introducing two extra ancillary spins coupled to the main
chain at the boundaries, which makes the problem {\it{integrable}}. The
eigenstates of the transverse field XY chain can be obtained by proper
projection in the enlarged chain. Using this mapping, we are able to calculate
the entanglement entropy of the transverse field XY chain using the usual
correlation matrix technique up to relatively large sizes.
