Probabilistic quantum logic operations using polarizing beam splitters - art. no. 062311

It has preciously been shown that probabilistic quantum logic operations ma y be performed using linear optical elements. additional photons (ancilla), and post-selection based on the output of single-photon detectors. Here we describe the operation of several quantum logic operations of an elementar y nature, including a quantum parity check and a quantum encoder, and we sh ow how they may be combined to implement a controlled-NOT (CNOT) gate. All of these gates may be constructed using polarizing beam splitters that comp letely transmit one state of polarization and totally, reflect the orthogon al state of polarization, which allows a simple explanation of each operati on. We also describe a polarizing beam splitter implementation of a CNOT La te that is closely analogous to the quantum teleportation technique preciou sly suggested by Gottesman and Chuang [Nature 402, 390 (1999)]. Finally. ou r approach has the interesting feature that it makes practical use of a qua ntum-eraser technique.