A setup is proposed in which the number-state expansion of a one-mode traveling-wave optical field is truncated so as to leave its vacuum, one-, and two-photon components. The process is a realization of quantum teleportation on a three-state basis. The possibility of generalization to the first n components is also considered.
A recent work [Pegg et al., Phys. Rev. Lett. 81, 1604 (1998)] showed how to generate a running-wave superposition of zero- and one-photon field states, C0∣0〉+C1∣1〉, by physical truncation of the photon number superposition making up a coherent state. Here we discuss the extension of this device to the case of N components: ${C}_{0}|0〉{+C}_{1}|1〉+\ensuremath{\cdot}\ensuremath{\cdot}\ensuremath{\cdot}{+C}_{N}|N〉.$
We employ the quantum state of a single photon entangled with the vacuum (| GROUP ⟩ A | GROUP ⟩ B − | GROUP ⟩ A | GROUP ⟩ B ), generated by a photon incident upon a symmetric beam splitter, to teleport single-mode quantum states of light by means of the Bennett protocol. The teleportation of coherent states results in the truncation of their Fock expansion to the first two terms. We analyze the teleported ensembles by means of homodyne tomography and obtain fidelities of up to 99 per cent for low-source state amplitudes. This work is an experimental realization of the quantum scissors device proposed by Pegg, Phillips and Barnett ( Phys. Rev. Lett. , 81 (1998) 1604).
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 that selectively removes specific Fock states, making holes in the Fock-state expansion of the input field.
We suggest a scheme of conditional teleportation of quantum states of optical fields using squeezers and photon counting. Alice feeds the mode whose state is desired to be teleported and one mode of a two-mode squeezed vacuum into a parametric amplifier, and detects output photon numbers. The result is then communicated to Bob, who shifts the photon number of his part accordingly. We show that for some classes of states the method can yield, with reasonable success probability, a teleportation fidelity close to unity. The method represents a modification of a recently proposed scheme [G. J. Milburn and S. L. Braunstein, Phys. Rev. A 60, 937 (1999)], where measurements of the photon-number difference and the phase sum are considered. The present scheme brings the method closer to the current experimental techniques.