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Journal of Physics B Atomic Molecular and Optical Physics

Generating entangled states of continuous variables via cross-Kerr nonlinearity

Zhi‐Ming Zhang, Ashfaq H. Khosa, Manzoor Ikram, Muhammad Suhail Zubairy

Published May 3, 2007• 11 citations
Publisher

Abstract

We propose a scheme for generating entanglement of quantum states with continuous variables (coherent states and squeezed vacuum states) of electromagnetical fields. The scheme involves cross-Kerr nonlinearity. It was shown that the cross-Kerr nonlinearity required for generating the superposition and entanglement of squeezed vacuum states is smaller than that required for coherent states. It was also found that the fidelity monotonously decreases with both the increase of the amplitude of the input coherent field and the increase of the deviation of the nonlinear phase shift from π.

DOI
10.1088/0953-4075/40/10/024

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We propose a scheme for generating entanglement of quantum states with continuous variables (coherent states and squeezed vacuum states) of electromagnetical fields. The scheme involves cross-Kerr nonlinearity. It was shown that the cross-Kerr nonlinearity required for generating the superposition and entanglement of squeezed vacuum states is smaller than that required for coherent states. It was also found that the fidelity monotonously decreases with both the increase of the amplitude of the input coherent field and the increase of the deviation of the nonlinear phase shift from π.
We propose a scheme for generating the superposition and the entanglement of squeezed vacuum states of electromagnetical fields. The scheme involves single-photon source, single photon detector, and cross Kerr nonlinearity. The Kerr nonlinearity required for generating the superposition of squeezed vacuum states is 1/2 of that required for generating the superposition of coherent states. The proposal can also be extended to generate the entanglement states between two coherent states and that between one coherent state and one squeezed vacuum state.
We propose methods for generating Bell-type entangled coherent states for quantum information processing. The protocols are completed using linear optical elements, single-photon detectors, and cross-Kerr nonlinearity. We investigate the decoherence effect on our protocols; photon loss is found to affect only the probability, not the fidelity, of the generation process. The entanglement of the generated entangled states is also analyzed using concurrence. Finally, the feasibility of our scheme is discussed using the continuous-time cross-phase modulation model. In the weak nonlinearity region, on the condition that θ2|αp|2∼1, θ≪1, and σ2≪1, our scheme is applicable theoretically.
We propose a scheme for generating entangled states of light fields. This scheme only requires the cross-Kerr nonlinear interaction between coherent light-beams, followed by a homodyne detection. Therefore, this scheme is within the reach of current technology. We study in detail the generation of the entangled states between two modes, and that among three modes. In addition to the Bell states between two modes and the W states among three modes, we find plentiful new kinds of entangled states. Finally, the scheme can be extend to generate the entangled states among more than three modes.
We propose a protocol for creating arbitrary qudit state (including entangled states) with arbitrary dimensionality in continuous variable system using weak cross-Kerr nonlinearity, linear beamsplitters, detectors not resolving photon numbers, and sources of coherent states. The equation for unique determination of the used coherent states amplitudes is found. The protocol is applicable for creating entangled states at distances of 100 km using cross-Kerr nonlinearity χ ≥ χ min ≃ 0.01 and optical fiber quantum channel.
We propose a scheme for generating entangled states of light fields. This scheme only requires the cross-Kerr nonlinear interaction between coherent light beams, followed by a homodyne detection. Therefore, this scheme is within the reach of current technology. We study in detail the generation of the entangled states between two modes, and that among three modes. In addition to the Bell states between two modes and the W states among three modes, we find plentiful new kinds of entangled states. Finally, the scheme can be extended to generate the entangled states among more than three modes.