A method comprising: receiving an input polarized beam having a first relative magnitude and a first relative polarization angle, wherein the input polarized beam represents a first logic state or a second logic state based on the first relative polarization angle and the first relative magnitude; splitting the input polarized beam into a first beam and a second beam, wherein the first beam and the second beam equal or nearly equal and represent the same logic state as the input polarized beam, wherein the relative polarization angle and relative magnitude of the first beam equal or nearly equal the first relative polarization angle and the first relative magnitude, respectively, of the input polarized beam, and wherein the relative polarization angle and relative magnitude of the second beam equal or nearly equal the first relative polarization angle and the first relative magnitude, respectively, of the input polarized beam; polarizing the first beam and the second beam such that the difference between the relative polarization angle of the polarized first beam and the relative polarization angle of the polarized second beam is 180 degrees or nearly 180 degrees; optically eliminating or nearly optically eliminating the first beam if the relative polarization angle of the first beam represents the second logic state, wherein the first beam is optically maintained if the relative polarization angle of the first beam represents the first logic state; and optically eliminating or nearly optically eliminating the second beam if the relative polarization angle of the second beam represents the first logic state, wherein the second beam is optically maintained if the relative polarization angle of the second beam represents the second logic state. receiving an input polarized beam having a first relative magnitude and a first relative polarization angle, wherein the input polarized beam represents a first logic state or a second logic state based on the first relative polarization angle and the first relative magnitude; splitting the input polarized beam into a first beam and a second beam, wherein the first beam and the second beam equal or nearly equal and represent the same logic state as the input polarized beam, wherein the relative polarization angle and relative magnitude of the first beam equal or nearly equal the first relative polarization angle and the first relative magnitude, respectively, of the input polarized beam, and wherein the relative polarization angle and relative magnitude of the second beam equal or nearly equal the first relative polarization angle and the first relative magnitude, respectively, of the input polarized beam; polarizing the first beam and the second beam such that the difference between the relative polarization angle of the polarized first beam and the relative polarization angle of the polarized second beam is 180 degrees or nearly 180 degrees; optically eliminating or nearly optically eliminating the first beam if the relative polarization angle of the first beam represents the second logic state, wherein the first beam is optically maintained if the relative polarization angle of the first beam represents the first logic state; and optically eliminating or nearly optically eliminating the second beam if the relative polarization angle of the second beam represents the first logic state, wherein the second beam is optically maintained if the relative polarization angle of the second beam represents the second logic state. <EOS>