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Scientific Reports

Highly efficient hyperentanglement concentration with two steps assisted by quantum swap gates

Bao‐Cang Ren, Gui Lu Long

Published Nov 10, 2015• 34 citations
Publisher

Abstract

We present a two-step hyperentanglement concentration protocol (hyper-ECP) for polarization-spatial hyperentangled Bell states based on the high-capacity character of hyperentanglement resorting to the swap gates, which is used to obtain maximally hyperentangled states from partially hyperentangled pure states in long-distance quantum communication. The swap gate, which is constructed with the giant optical circular birefringence (GOCB) of a diamond nitrogen-vacancy (NV) center embedded in a photonic crystal cavity, can be used to transfer the information in one degree of freedom (DOF) between photon systems. By transferring the useful information between hyperentangled photon pairs, more photon pairs in maximally hyperentangled state can be obtained in our hyper-ECP, and the success probability of the hyper-ECP is greatly improved. Moreover, we show that the high-fidelity quantum gate operations can be achieved by mapping the infidelities to heralded losses even in the weak coupling regime.

DOI
10.1038/srep16444

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We present a two-step hyperentanglement concentration protocol (hyper-ECP) for polarization-spatial hyperentangled Bell states based on the high-capacity character of hyperentanglement resorting to the swap gates, which is used to obtain maximally hyperentangled states from partially hyperentangled pure states in long-distance quantum communication. The swap gate, which is constructed with the giant optical circular birefringence (GOCB) of a diamond nitrogen-vacancy (NV) center embedded in a photonic crystal cavity, can be used to transfer the information in one degree of freedom (DOF) between photon systems. By transferring the useful information between hyperentangled photon pairs, more photon pairs in maximally hyperentangled state can be obtained in our hyper-ECP, and the success probability of the hyper-ECP is greatly improved. Moreover, we show that the high-fidelity quantum gate operations can be achieved by mapping the infidelities to heralded losses even in the weak coupling regime.
Entanglement concentration protocol (ECP) is used to extract the maximally entangled states from less entangled pure states. Here we present a general hyperconcentration protocol for two-photon systems in partially hyperentangled Bell states that decay with the interrelation between the time-bin and the polarization degrees of freedom (DOFs), resorting to an input-output process with respect to diamond nitrogen-vacancy centers coupled to resonators. We show that the resource can be utilized sufficiently and the success probability is largely improved by iteration of the hyper-ECP process. Besides, our hyper-ECP can be directly extended to concentrate nonlocal partially hyperentangled N-photon Greenberger-Horne-Zeilinger states, and the success probability remains unchanged with the growth of the number of photons. Moreover, the time-bin entanglement is a useful DOF and it only requires one path for transmission, which means it not only economizes on a large amount of quantum resources but also relaxes from the path-length dispersion in long-distance quantum communication.
Hyperentanglement has attracted much attention due to its fascinating applications in quantum communication. However, it is impossible to purify a pair of photon systems in a mixed hyperentangled state with errors in two degrees of freedom using linear optical elements only, far different from all the existing entanglement purification protocols in a degree of freedom (DOF) for quantum systems. Here, we investigate the possibility of purifying a spatial-polarization mixed hyperentangled Bell state with the errors in both the spatial-mode and polarization DOFs, resorting to the nonlinear optics of a nitrogen-vacancy (NV) center in a diamond embedded in a photonic crystal cavity coupled to a waveguide. We present the first hyperentanglement purification protocol for purifying a pair of two-photon systems in a mixed hyperentangled Bell state with the errors in two DOFs. We also propose an efficient hyperentanglement concentration protocol for a partially hyperentangled Bell pure state, which has the maximal success probability in principle. These two protocols are useful in long-distance quantum communication with hyperentanglement.
Recently, two-photon six-qubit hyperentangled states were produced in experiment and they can improve the channel capacity of quantum communication largely. Here we present a scheme for the hyperentanglement purification of nonlocal two-photon systems in three degrees of freedom (DOFs), including the polarization, the first-longitudinal-momentum, and the second-longitudinal-momentum DOFs. Our hyperentanglement purification protocol (hyper-EPP) is constructed with two steps resorting to parity-check quantum nondemolition measurement on the three DOFs and swap gates, respectively. With these two steps, the bit-flip errors in the three DOFs can be corrected efficiently. Also, we show that using swap gates is a universal method for hyper-EPP in the polarization DOF and multiple-longitudinal-momentum DOFs. The implementation of our hyper-EPP is assisted by nitrogen-vacancy centers in optical microcavities, which could be achieved with current techniques. It is useful for long-distance high-capacity quantum communication with two-photon six-qubit hyperentanglement.
Hyperentanglement is a promising resource in quantum information processing, especially for increasing the channel capacity of long-distance quantum communication. Here we present a general hyper-entanglement concentration protocol (hyper-ECP) for nonlocal partially hyperentangled Bell states that decay with the interrelationship between the polarization and the spatial-mode degrees of freedom of two-photon systems, which is not taken into account in other hyper-ECPs, resorting to the optical property of the quantum-dot spins inside one-side optical microcavities. We show that the success probability of our hyper-ECP is largely increased by iteration of the hyper-ECP process. Our hyper-ECP can be straightforwardly generalized to distill nonlocal maximally hyperentangled N-photon Greenberger-Horne-Zeilinger (GHZ) states from arbitrary partially hyperentangled GHZ-class states.
Recently, two-photon six-qubit hyperentanged states were produced in experiment and they can improve the channel capacity of quantum communication largely. Here we present the first scheme for the hyperentanglement purification of nonlocal two-photon systems in three degrees of freedom (DOFs), including the polarization, the first longitudinal momentum, and the second longitudinal momentum DOFs. Our hyper-EPP is constructed with two steps resorting to parity-check quantum nondemolition measurement on the three DOFs and SWAP gates, respectively. With these two steps, the bit-flip errors in the three DOFs can be corrected efficiently. Using SWAP gates is a universal method for hyper-EPP in the polarization DOF and multiple longitudinal momentum DOFs. The implementation of our hyper-EPP is assisted by nitrogen-vacancy centers in optical microcavities, which could be achieved with current techniques. It is useful for long-distance high-capacity quantum communication with two-photon six-qubit hyperentanglement.
We present an efficient hyperentanglement concentration protocol (hyper-ECP) for two-photon six-qubit systems in nonlocal partially hyperentangled Bell states with unknown parameters. In our scheme, we use two identical partially hyperentangled states which are simultaneously entangled in polarization and two different longitudinal momentum degrees of freedom (DOFs) to distill the maximally hyperentangled Bell state. The quantum nondemolition detectors based on the cross-Kerr nonlinearity are used to realize the parity checks of two-photon systems in three DOFs. The hyper-ECP can extract all the useful entanglement source, and the success probability can reach the theory limit with the help of iteration. All these advantages make our hyper-ECP useful in long-distance quantum communication in the future.