  Fully polarized nonlinear Breit-Wheeler pair production from a beam of
polarized seed photons is investigated in pulsed plane-wave backgrounds. The
particle (electron and positron) spin and photon polarization are
comprehensively described with the theory of the density matrix. The compact
expressions for the energy spectrum and spin polarization of the produced
particles, depending on the initial polarization of the seed photon beam, are
derived and discussed in both linearly and circularly polarized laser
backgrounds. The numerical results suggest an appreciable improvement of the
positron yield by orthogonalizing the photon polarization to the laser
polarization, and the generation of a highly polarized positron beam from a
beam of circularly polarized seed photons. The locally monochromatic
approximation and the locally constant field approximation are derived and
benchmarked with the full quantum electrodynamic calculations.
