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.
Highlights
The swap gate is constructed with the giant optical circular birefringence (GOCB, defined as the differences in effective refractive index, phase, or reflection/transmission coefficients between the two circular polarizations38) of a nitrogen-vacancy (NV) center in a diamond embedded in the evanescent field of a photonic crystal cavity coupled to a waveguide, and it can be used to transfer the information in the polarization DOF between photon systems in the hyperentangled states
In the previous hyper-ECPs, the polarization states and the spatial-mode states are concentrated independently with polarization parity-check quantum nondemolition detector (P-QND) and spatial-mode parity-check quantum nondemolition detector (S-QND), respectively, where the success probability is limited without the information transfer within the hyperentangled photon pairs
Our calculation shows that high-fidelity basic quantum gate operations can be achieved by mapping the infidelities to heralded losses even in the weak coupling regime. This two-step hyper-ECP with swap gates is very useful for obtaining maximally hyperentangled states in the long-distance high-capacity quantum communication protocols based on several DOFs of photon systems
Summary
In 2008, Sheng and Deng[18] proposed a high-efficiency ECP for photon systems in a partially entangled Bell state by iterative application of the ECP process, resorting to nonlinear optical elements. By using the nonlinear optical elements, the success probability of the hyper-ECP with the Schmidt projection method can be improved by resorting to the iteration protocol[14,19] These hyper-ECPs for photon systems were implemented by concentrating the polarization states and the spatial-mode states independently. Our calculation shows that high-fidelity basic quantum gate operations can be achieved by mapping the infidelities to heralded losses even in the weak coupling regime This two-step hyper-ECP with swap gates is very useful for obtaining maximally hyperentangled states in the long-distance high-capacity quantum communication protocols based on several DOFs of photon systems
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