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International Journal of Quantum Information

Generation of four-photon polarization entangled states with cross-Kerr nonlinearity

Meiyu Wang, Fengli Yan

Published May 29, 2015• 1 citation
Publisher

Abstract

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.

DOI
10.1142/s0219749915500240

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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.
Abstract We propose a theoretical protocol for preparing four-photon polarization entangled decoherence-free states, which are immune to the collective noise. With the assistance of the cross-Kerr nonlinearities, a two-photon spatial entanglement gate, two controlled-NOT gates, a four-photon polarization entanglement gate are inserted into the circuit, where X homodyne measurements are aptly applied. Combined with some swap gates and simple linear optical elements, four-photon polarization entangled decoherence-free states which can be utilized to represent two logical qubits, |0〉L and |1〉L are achieved at the output ports of the circuit. This generation scheme may be implemented with current experimental techniques.
We propose two schemes for preparing four-photon cluster state through cross-Kerr nonlinearity. Two coherent fields interact when they enter a nonlinear Kerr medium. If the interaction time is chosen appropriately in each Kerr medium, four-photon cluster state can be generated based on the results of two homodyne detectors in the first scheme. These schemes only use Kerr medium and homodyne measurements on coherent light fields, which can be efficiently made in quantum optical laboratories. In addition, weak cross-Kerr nonlinearity is sufficient. All of the properties make these schemes feasible in experiments.
A scheme is presented for preparing maximally entangled states among six modes.The scheme only utilizes weak cross-Kerr nonlinearity and momentum quadrature homodyne measurements on the probe mode of intense coherent light fields.It is relatively easy to generate Dicke states and W states of light fields in the scheme.It is not necessary that the cross-Kerr nonlinearity is very large,as long as the coherent light is bright enough.Therefore,this scheme is within the reach of current technology.In addition,only weak coherent light beams,with which single-photon sources have been replaced in the signal modes,are needed in the present scheme since it is difficult to realize single-photon sources in experiments.