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It has previously been shown that probabilistic quantum logic operations canbe performed using linear optical elements, additional photons (ancilla), andpost-selection based on the output of single-photon detectors. Here we describethe operation of several quantum logic operations of an elementary nature,including a quantum parity check and a quantum encoder, and we show how theycan be combined to implement a controlled-NOT (CNOT) gate. All of these gatescan be constructed using polarizing beam splitters that completely transmit onestate of polarization and totally reflect the orthogonal state of polarization,which allows a simple explanation of each operation. We also describe apolarizing beam splitter implementation of a CNOT gate that is closelyanalogous to the quantum teleportation technique previously suggested byGottesman and Chuang [Nature 402, p.390 (1999)]. Finally, our approach has theinteresting feature that it makes practical use of a quantum-eraser technique.Comment: 9 pages, RevTex; Submitted to Phys. Rev. A; additional references  inlcude

Probabilistic quantum logic operations using polarizing beam splitters