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Journal of Physics B Atomic Molecular and Optical Physics

Entanglement purification based on photonic polarization parity measurements

Song Xin-Guo, Xun‐Li Feng, L. C. Kwek, C. H. Oh

Published Jul 25, 2005• 8 citations
Publisher

Abstract

We present an entanglement purification protocol for photonic mixed entangled states based on the two-mode polarization nondemolition parity detectors. Without the use of the controlled-NOT (CNOT) operations, the efficiency of our protocol can nearly approach that of the CNOT protocol. The total successful probability of our protocol can be nearly enhanced to the quantity twice as large as that of the linear-optics-based protocol. Besides, our protocol adopts common photon detectors rather than the sophisticated single-photon detectors required in the linear-optics-based protocol.

DOI
10.1088/0953-4075/38/15/018

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We present an entanglement purification protocol for photonic mixed entangled states based on the two-mode polarization nondemolition parity detectors. Without the use of the controlled-NOT (CNOT) operations, the efficiency of our protocol can nearly approach that of the CNOT protocol. The total successful probability of our protocol can be nearly enhanced to the quantity twice as large as that of the linear-optics-based protocol. Besides, our protocol adopts common photon detectors rather than the sophisticated single-photon detectors required in the linear-optics-based protocol.
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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 present an efficient entanglement purification protocol (EPP) with controlled-not (CNOT) gates and linear optics. With the CNOT gates, our EPP can reach a higher fidelity than the conventional one. Moreover, it does not require the fidelity of the initial mixed state to satisfy F > 1/2. If the initial state is not entangled, it still can be purified. With the linear optics, this protocol can get pure maximally entangled pairs with some probabilities. Meanwhile, it can be used to purify the entanglement between the atomic ensembles in distant locations. This protocol may be useful in long-distance quantum communication.
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.
We describe an entanglement purification protocol for a polarization Bell state. Different from the previous protocols, it does not require the controlled-not gate, and only uses linear optical elements to complete the task. This protocol requires multi-copy degraded mixed states, which can make this protocol obtain a high fidelity in one purification step. It can also be extended to purify the multi-photon Greenberger–Horne–Zeilinger (GHZ) state. This protocol may be useful in future long-distance communication.