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Abstract
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.
Highlights
DOF11, be used to teleport the unknown quantum state in two DOFs21 and complete the hyperentanglement swapping between two photonic quantum systems without entanglement[22], and help to design the deterministic hyperentanglement purification[11,12,13,14] which solves the troublesome problem that the parties in quantum repeaters should sacrifice a large amount of quantum resources with conventional entanglement purification protocols (EPPs)[9,10] as the deterministic EPPs11–14 work in a completely deterministic way[25,26,27]
We show that our hyper-ECP is suitable for arbitrary partially hyperentangled N-photon GHZ states, and the success probability is still unchanged with the growth of the number of photons
An nitrogen vacancy (NV) center in diamond is created by a replaceable nitrogen atom substituting for a carbon atom and an adjacent vacancy in the diamond lattice
Summary
DOF11, be used to teleport the unknown quantum state in two DOFs21 and complete the hyperentanglement swapping between two photonic quantum systems without entanglement[22], and help to design the deterministic hyperentanglement purification[11,12,13,14] which solves the troublesome problem that the parties in quantum repeaters should sacrifice a large amount of quantum resources with conventional entanglement purification protocols (EPPs)[9,10] as the deterministic EPPs11–14 work in a completely deterministic way[25,26,27]. In 2013, Ren et al.[28] proposed the first hyper-ECP for two-photon systems in polarization-spatial less-hyperentangled states with linear optical elements only, including the cases for the nonlocal photonic quantum systems with known and unknown parameters, respectively. They proposed the parameter-splitting method[28], a fascinating method, to extract the maximally entangled photons when the coefficients of the initial partially entangled state are known, and this method is very efficient and simple in terms of concentrating partially entangled state as it can be achieved with the maximum success probability by performing the protocol only once. We show that our hyper-ECP is suitable for arbitrary partially hyperentangled N-photon GHZ states, and the success probability is still unchanged with the growth of the number of photons
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