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.
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.
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.
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.
As the interaction between the photons and the environment which will make the entangled photon pairs in less entangled states or even in mixed states, the security and the efficiency of quantum communication will decrease. We present an efficient hyperentanglement purification protocol that distills nonlocal high-fidelity hyper-entangled Bell states in both polarization and spatial-mode degrees of freedom from ensembles of two-photon system in mixed states using linear optics. Here, we consider the influence of the photon loss in the channel which generally is ignored in the conventional entanglement purification and hyperentanglement purification (HEP) schemes. Compared with previous HEP schemes, our HEP scheme decreases the requirement for nonlocal resources by employing high-dimensional mode-check measurement, and leads to a higher fidelity, especially in the range where the conventional HEP schemes become invalid but our scheme still can work.
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.
We investigate a new approach for achieving hyperdistillation and hyperentanglement purification operations simultaneously on two-photon systems, whose state is described by nonlocal hyperentangled Bell states on both the spatial mode and polarization degree of freedoms. Exploiting linear optics and local entanglement resource, the quantum nondemolition (QND) parity-checking measurement and the heralded two-qubit amplification could are key steps in our scheme. With the QND parity-checking measurement and heralded qubit amplification operations, both the bit-flip (phase-flip) errors caused by decoherence in noisy channels and the vacuum errors caused by the transmission losses can be corrected. We show that the proposed scheme provides a new solution to overcome the problem of photon losses and decoherence simultaneously, which could be achieved with current technologies.
Photon system is a promising candidate for quantum information processing, and it can be used to achieve some important tasks with the interaction between a photon and an atom (or a artificial atom), such as the transmission of secret information, the storage of quantum states, and parallel quantum computing. Several degrees of freedom (DOFs) of a photon system can be used to carry information in the realization of quantum information processing, such as the polarization, spatial-mode, orbit-angular-momentum, time-bin, and frequency DOFs. A hyperparallel quantum computer can implement the quantum operations on several DOFs of a quantum system simultaneously, which reduces the operation time and the resources consumed in quantum information processing. The hyperparallel quantum operations are more robust against the photonic dissipation noise than the quantum computing in one DOF of a photon system. Hyperentanglement, defined as the entanglement in several DOFs of a quantum system, can improve the channel capacity and the security of long-distance quantum communication, and it can also be conductive to completing some important tasks in quantum communication. Hyperentangled Bell-state analysis is used to completely distinguish the 16 hyperentangled Bell states, which is very useful in high-capacity quantum communication protocols and quantum repeaters. In order to depress the effect of noises in quantum channel, hyperentanglement concentration and hyperentanglement purification are required to improve the entanglement of the quantum systems in long-distance quantum communication, which is also very useful in high-capacity quantum repeaters. Hyperentanglement concentration is used to distill several nonlocal photon systems in a maximally hyperentangled state from those in a partially hyperentangled pure state, and hyperentanglement purification is used to distill several nonlocal photon systems in a high-fidelity hyperentangled state from those in a mixed hyperentangled state with less entanglement. In this reviewing article, we review some new applications of photon systems with multiple DOFs in quantum information processing, including hyperparallel photonic quantum computation, hyperentangled-Bell-state analysis, hyperentanglement concentration, and hyperentanglement purification.