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arXiv:quant-ph/0210096 · Physical Review A

Linear optical implementation of a single-mode quantum filter and generation of multiphoton polarization entangled states

Xu‐Bo Zou, K. Pahlke, Wolfgang M. Mathis

Published Dec 26, 2002• 13 citations
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Abstract

We propose a scheme to implement a single-mode quantum filter, which selectively eliminates the one-photon state in a quantum state $\ensuremath{\alpha}|0〉+\ensuremath{\beta}|1〉+\ensuremath{\gamma}|2〉.$ The vacuum state and the two-photon state are transmitted without any change. This scheme requires single-photon sources, linear optical elements, and photon detectors. Furthermore, we demonstrate how this filter can be used to realize a two-qubit projective measurement and to generate multiphoton polarization entangled states.

DOI
10.1103/physreva.66.064302

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We propose a scheme to implement a single-mode quantum filter, which selectively eliminates the one-photon state in a quantum state \ensuremathα∣0〉+\ensuremathβ∣1〉+\ensuremathγ∣2〉.\ensuremath{\alpha}|0〉+\ensuremath{\beta}|1〉+\ensuremath{\gamma}|2〉.\ensuremathα∣0〉+\ensuremathβ∣1〉+\ensuremathγ∣2〉. The vacuum state and the two-photon state are transmitted without any change. This scheme requires single-photon sources, linear optical elements, and photon detectors. Furthermore, we demonstrate how this filter can be used to realize a two-qubit projective measurement and to generate multiphoton polarization entangled states.
We propose a feasible scheme to create nnn-party (n≥2n\geq 2n≥2) polarization-entangled photon states in a controllable way. The scheme requires only single-photon sources, single-photon quantum non-demolition measurement (SP-QNDM) and simple linear optical elements, usually with high perfections. The SP-QNDM acts as a non-destructive projection measurement onto the wanted entangled states and filters out the unwanted terms. Our scheme in fact realizes entanglement of non-interacting photons; the interaction occurs only implicitly in the optical elements and SP-QNDM. We also briefly consider purification of mixed single-photon states within our scheme.
We propose a linear optical scheme to implement the nondeterministic two-qubit controlled phase gate with the certain success probability. The proposed setup involves simple linear optical elements, a pair of the two-photon polarization entangled states, and the conventional photon detectors that only distinguish the vacuum and nonvacuum Fock number states. A sophisticated single-photon detector distinguishing one or two photon states is unnecessary. This can greatly simplify the experimental realization of a linear optical quantum computer.
We report an experimental implementation of deterministic preparation and measurement of single-photon two-qubit entangled states, in which the polarization and the spatial modes of a single-photon each represent a quantum bit. It is demonstrated that all four single-photon two-qubit entangled states (Bell states) can be easily prepared and measured deterministically using linear optical elements alone. We also discuss how this scheme can be used for implementing recently proposed single-photon two-qubit quantum cryptography.
We implement experimentally a deterministic method to prepare and measure the so-called single-photon two-qubit entangled states or single-photon Bell states, in which the polarization and the spatial modes of a single photon each represent a quantum bit. All four single-photon Bell states can be easily prepared and measured deterministically using linear optical elements alone. We also discuss how this method can be used for the recently proposed single-photon two-qubit quantum cryptography scheme.
We present a scheme to generate the polarization-entangled two-photon state 1/2(∣H〉∣V〉+∣V〉∣H〉),1/\sqrt{2}(|H〉|V〉+|V〉|H〉),1/2​(∣H〉∣V〉+∣V〉∣H〉), which is of much interest in the field of quantum information processing. Furthermore, we demonstrate the capability of this concept in respect of a generalization to entangle N-photon states for interferometry and lithography. This scheme requires single-photon sources, linear optical elements, and a multifold coincidence detection.