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arXiv:0903.0468 · Journal of Physics B Atomic Molecular and Optical Physics

Production of genuine entangled states of four atomic qubits

Guiyun Liu, Le‐Man Kuang

Published Jul 27, 2009• 21 citations
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Abstract

We propose an optical scheme to generate genuine entangled states of four atomic qubits in optical cavities using a single-photon source, beam splitters and single-photon detectors. We demonstrate how to generate deterministically 16 orthonormal and independent genuine entangled states of four atomic qubits. It is found that the 16 genuine entangled states form a new type of representation of the four-atomic-qubit system, i.e. the genuine entangled-state representation. This representation brings a new interesting insight into better understanding of multipartite entanglement.

DOI
10.1088/0953-4075/42/16/165505

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We propose an optical scheme to generate genuine entangled states of four atomic qubits in optical cavities using a single-photon source, beam splitters and single-photon detectors. We demonstrate how to generate deterministically 16 orthonormal and independent genuine entangled states of four atomic qubits. It is found that the 16 genuine entangled states form a new type of representation of the four-atomic-qubit system, i.e. the genuine entangled-state representation. This representation brings a new interesting insight into better understanding of multipartite entanglement.
A simple experimental scheme is proposed to generate a three-photon entangled WWW state and a genuine four-photon entangled state $|{\ensuremath{\chi}}^{00}⟩$ that has many interesting entanglement properties and possible applications in quantum information processing. These multipartite entangled states can be generated with a certain success probability. We show that even when the quantum efficiency of the detector is $\ensuremath{\eta}=0.75$, the success probability can reach $2.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ for WWW-state production and $3.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ for $|{\ensuremath{\chi}}^{00}⟩$-state production. The scheme is based only on simple linear optical elements and conventional photon detectors, which greatly decrease the experimental difficulty of implementing linear optical quantum computation.
Based on the interference effect of polarized photons leaking out of separate cavities, we propose schemes for the generation of the N -atom Greenberger–Horne–Zeilinger (GHZ) state, three-atom W state and a genuine four-atom entangled state |χ⟩. In these schemes, each of the atoms is trapped separately in a remote optical cavity, and the possible spontaneous channels induced by the excited atoms lead to the coherent superposition of the states of the atoms. The desired multipartite entangled states can be generated with a certain success probability by the subsequent detection of the polarized photons in different modes. The schemes would be useful steps towards long-distance quantum communication, distributed quantum computation and constructing remote quantum information processing networks.
We present a scheme to produce an entangled four-photon W state by using linear optical elements. The symmetrical setup of linear optical elements consists of four beam splitters, four polarization beam splitters, and four mirrors. A photon Einstein-Podolsky-Rosen pair and two single photons are required as the input modes. The projection on the W state can be made by a four-photon coincidence measurement. Further, we show that by means of a horizontally oriented polarizer in front of one detector, the W state of three photons can be generated.
We show how to prepare three different types of four-photon polarization entangled states among four modes. The scheme only use cross-Kerr medium, polarization beam splitters and X homodyne measurements on coherent light fields, which can be efficiently implemented in quantum optical laboratories. GHZ states and symmetric Dick states can be generated in deterministic way based on the scheme. With the possible availability of suitable strong Kerr nonlinearity, another type of entangled state called genuine four-photon entangled state can be realized as well.
We propose an optical scheme to generate cluster states of atomic qubits, with each trapped in separate optical cavity, via atom-cavity-laser interaction. The quantum information of each qubit is encoded on the degenerate ground states of the atom, hence the entanglement between them is relatively stable against spontaneous emission. A single-photon source and two classical fields are employed in the present scheme. By controlling the sequence and time of atom-cavity-laser interaction, we show that the atomic cluster states can be produced deterministically.