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Quantum Information and Computation

Polarization-entanglement purification and concentration using cross-Kerr nonlinearity

Chuan Xi Wang, Yong Zhang, Guang-Sheng Jin

Published Nov 1, 2011• 57 citations
Publisher

Abstract

We present an entanglement purification protocol and an entanglement concentration protocol in this paper, resorting to cross-Kerr nonlinearities and interference of two coherent beams. Our purification protocol can be used to purify photon pairs not only from an ideal entangled source but also from a parametric down-conversion source by the measurement on the interference of two coherent beams without giant cross-Kerr media. Our quantum nondemolition detection can also used to concentrate photon pairs in less entangled pure states efficiently. Our protocols are more flexibilities in distinguishing the phases of the coherent states during homodyne detection.

DOI
10.26421/qic11.11-12-8

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We present an entanglement purification protocol and an entanglement concentration protocol in this paper, resorting to cross-Kerr nonlinearities and interference of two coherent beams. Our purification protocol can be used to purify photon pairs not only from an ideal entangled source but also from a parametric down-conversion source by the measurement on the interference of two coherent beams without giant cross-Kerr media. Our quantum nondemolition detection can also used to concentrate photon pairs in less entangled pure states efficiently. Our protocols are more flexibilities in distinguishing the phases of the coherent states during homodyne detection.
We present a way for entanglement purification based on two parametric down-conversion (PDC) sources with cross-Kerr nonlinearities. It is comprised of two processes. The first one is a primary entanglement purification protocol for PDC sources with nondestructive quantum nondemolition (QND) detectors by transferring the spatial entanglement of photon pairs to their polarization. In this time, the QND detectors act as the role of controlled-NOT (CNOT) gates. Also they can distinguish the photon number of the spatial modes, which provides a good way for the next process to purify the entanglement of the photon pairs kept more. In the second process for entanglement purification, new QND detectors are designed to act as the role of CNOT gates. This protocol has the advantage of high yield and it requires neither CNOT gates based on linear optical elements nor sophisticated single-photon detectors, which makes it more convenient in practical applications.
We propose a protocol for realizing two entanglement concentration scheme with cross-Kerr nonlinearity and double cross-phase modulation method. In our protocols, two remote parties do not require the accurate information of the less entangled state and the double cross-phase modulation is introduced to overcome the errors caused by the imperfect Kerr interaction. By this way, a single-photon entanglement is concentrated, and a three-photon polarized GHZ state is also achieved. Furthermore this protocol can be scaled to multiphoton polarized GHZ state concentration and the giant Kerr media is not needed, which makes our protocols more feasible in experiment.
Abstract We show how to concentrate an arbitrary four-photon polarization entangled state into a maximally entangled state based on some quantum nondemolition detectors. The entanglement concentration protocol (ECP) resorts to an ancillary single-photon resource and the conventional projection measurement on photons to assist the concentration, which makes it more economical. Our ECP involves weak cross-Kerr nonlinearities, X homodyne measurement and basic linear-optical elements, which make it feasible in the current experimental technology. Moreover, the ECP considers cyclic utilization to enhance a higher success probability. Thus, our scheme is meaningful in practical applications in quantum communication.
In this paper, we propose two ways of Dicke state generation using single photons and weak coherent pulse resorting to Kerr nonlinearities. By interference of two coherent beams, the Dicke state are realized in polarization and photon number degrees of freedom. By performing homodyne detection on the coherent states, the multi-particle entangled Dicke state can be generated with a high probability. The realization of the protocols are more flexible as the phase differences can be easily distinguished during homodyne detection.
We present three protocols for directly measuring the concurrence of two-photon polarization-entangled states, including pure states and mixed states. Two signal photon pairs in the same polarization-entangled states are needed in each detection round, and the signal photons will pass through polarization-independent beam splitters simultaneously. The concurrence of the photon pairs will be encoded in the total probability of picking up the balanced states in the two output modes of the beam splitter, which can be directly measured by single-photon detectors. The photon detection efficiency can be further enhanced with the help of the weak cross-Kerr nonlinearity, and the signal photons will not be absorbed. The third scheme using the bilateral nondemolition measurements can measure the concurrence of both pure and mixed states with high efficiency and high fidelity and is robust against the copy error of the state to be measured. The sophisticated controlled-not operation of the previous schemes is not required here, so our protocols are more feasible within the current experimental technology.