Selective truncations of an optical state using projection synthesis

Selective truncation of the Fock-state expansion of an optical field can be achieved using projection synthesis. The process removes the predetermined Fock states from the input field by conditional measurement and teleportation. We present a scheme to perform projection synthesis based on multiport interferometry. This scheme can be used both as a generalized quantum scissors device that filters out Fock states with photon numbers higher than a predetermined value, and as a quantum punching device thqt selectively removes specific Fock states, making holes in the Fock-state expansion of the input field.