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Journal of Physics B Atomic Molecular and Optical Physics

Error correction of polarization entanglement in hyper-entangled state

Mei-Yu Wang, Fengli Yan, Ting Gao

Published Mar 3, 2020• 2 citations
Publisher

Abstract

Abstract We present two schemes for error-correction of polarization entanglement with time-bin entanglement and frequency entanglement in hyper-entangled state. In these two protocols, by performing the polarization parity-check operation, the bit-flip and phase-flip errors on the polarization part can be corrected and eliminated in one step. The parties in quantum communication can obtain maximally hyper-entangled states in two degrees of freedom in a deterministic way. Our protocols for purification are useful in practical applications for long-distance quantum communication.

DOI
10.1088/1361-6455/ab7c3c

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Abstract We present two schemes for error-correction of polarization entanglement with time-bin entanglement and frequency entanglement in hyper-entangled state. In these two protocols, by performing the polarization parity-check operation, the bit-flip and phase-flip errors on the polarization part can be corrected and eliminated in one step. The parties in quantum communication can obtain maximally hyper-entangled states in two degrees of freedom in a deterministic way. Our protocols for purification are useful in practical applications for long-distance quantum communication.
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Hyperentanglement is an effective quantum source for quantum communication network due to its high capacity, low loss rate, and its unusual character in teleportation of quantum particle fully. Here we present a deterministic error-correction scheme for nonlocal spatial-polarization hyperentangled photon pairs over collective-noise channels. In our scheme, the spatial-polarization hyperentanglement is first encoded into a spatial-defined time-bin entanglement with identical polarization before it is transmitted over collective-noise channels, which leads to the error rejection of the spatial entanglement during the transmission. The polarization noise affecting the polarization entanglement can be corrected with a proper one-step decoding procedure. The two parties in quantum communication can, in principle, obtain a nonlocal maximally entangled spatial-polarization hyperentanglement in a deterministic way, which makes our protocol more convenient than others in long-distance quantum communication.
We present a deterministic entanglement purification protocol (EPP) working with the currently available experiment techniques. In this protocol, we exploit the robust time-bin entanglement to purify the polarization entanglement determinately, which is quite different from the previous EPPs. After purification, the two parties in quantum communication can obtain a maximally entangled photon pair from each transmitted over a polarization-noise channel with a success probability of 100%, in principle. As the maximal polarization entanglement is of utmost importance in long-distance quantum communication, this protocol may be very useful in future applications.
Hyperentanglement is a promising resource in quantum information processing, especially for increasing the channel capacity of long-distance quantum communication. Hyperentanglement purification is an important method to obtain high-fidelity nonlocal hyperentangled states from mixed hyperentangled states in a long-distance quantum communication process with noisy channels. Here, we present a two-step hyperentanglement purification protocol for nonlocal mixed hyperentangled states with polarization bit-flip errors and spatial-mode phase-flip errors, resorting to polarization-spatial phase-check quantum nondemolition detectors and the quantum-state-joining method (QSJM). With QSJM, the protocol can preserve the states that are discarded in the previous hyperentanglement purification protocols. It has the advantage of a high efficiency, and it is useful for improving the entanglement of photon systems with several degrees of freedom in long-distance high-capacity quantum communication.
Entanglement purification is a powerful method to distill the high-quality entanglement from low-quality entanglement. In the paper, we propose an efficient two-step entanglement purification protocol (EPP) for the polarization entanglement by using only one copy of two-photon hyperentangled state in polarization, spatial-mode, and time-bin DOFs. We suppose that the entanglement in all DOFs suffer from channel noise. In two purification steps, the parties can reduce the bit-flip error and phase-flip error in polarization DOF by consuming the imperfect entanglement in the spatial-mode and time-bin DOFs, respectively. This EPP effectively reduces the consumption of entanglement pairs and the experimental difficulty. Moreover, if consider the practical photon transmission and detector efficiencies, our EPP has much higher purification efficiency than previous recurrence EPPs. Meanwhile, when one or two purification steps fail, the distilled mixed state may have residual entanglement. Taking use of the residual entanglement, the parties may still distill higher-quality polarization entanglement. Even if not, they can still reuse the residual entanglement in the next purification round. The existence of residual entanglement benefits for increasing the yield of the EPP. All the above advantages make our EPP have potential application in future quantum information processing.