High-Dimensional Quantum Non-Locality In Two-Photon Spatial Modes

Recently,Spatial light are widely applied in various region,including basic physics,classical physics and quantum physics,becoming the hot topic of the optical field.Comparing with polarization degree,spatial mode can form an orthogonal and complete basis to construct a high-dimensional Hilbert space,and thus provided higher resource and improve security in quantum information science.Key to realize high-dimensional quantum application is high-dimensional entangled states.Therefore,characterizing high-dimensional entangled states is of crucial importance in quantum information science and technology.On the other hand,the usually encountered approach to quantify the non-local feature of entanglement is the violation of a Bell-like inequality and demonstrating Hardy’s paradox.For this,we exploit two-photon entangled in spatial modes degree to quantify the non-local feature of high-dimensional entanglement.The main contents are as follows:1.Violation of a Bell inequality based on radial quantum number:Investigate the Bell inequalities for radial quantum number at the first time.We first focused on the nonlocal property of the radial spatial structure of a two-photon wave function.Except for orbital angular momentum,Laguerre-Gaussian(LG)mode possess another important index,that is radial quantum number,whose eigenstates can form an orthogonal and complete basis to construct a high-dimensional Hilbert space.Here,we demonstrate,both theoretically and experimentally,the violation of a suitable Clauser-Horne-Shimony-Holt(CHSH)Bell inequality for radial index p of the LG mode,thus manifesting the entanglement in the radial structure of two-photon wave functions.This work shows that the radial quantum number are other candidate to realize the encoding of high-dimensional quantum information,and possess important application prospects in high-dimensional quantum information region in the future.2.Hardy ’s paradox based on photonic orbital angular momentum:Experimentally realizing the general multisetting multidimensional version of Hardy’s paradox for the first time.Except for radial spatial structure,we also demonstrate high-dimensional entanglement of azimuthal spatial structure,i.e.,orbital angular momentum(OAM)of the LG mode.According to Chen’s proposal,we demonstrate that photon pairs generated by spontaneous parameter down-conversion process are entangled in high-dimensional OAM subspace,and thus show the Hardy’s paradox are available to quantify the nonlocal feature of entanglement.This work demonstrate that the nonlocal events increase with both dimension and setting,and thus nonclassical correlations can be made more robust to the presence of noise and other deleterious environmental effects.3.Hardy’s paradox based on angular-position correlation of two-photon:Experimentally demonstrate the multisetting high-dimensional version of Hardy’s paradox based on the strong angular position correlation of two-photon produced by down-conversion process.In our first work,we have verified the Hardy’s theorem can be used to quantify high-dimensional entanglement.Here,we introduce this theorem to angular position degree,and quantify the high-dimensional entanglement characteristics of angular-position for two-photon.This work shows evidently that angular variable can be consider as discrete variable to construct a larger but finite subspace,and could be expect to exploit some applicant quantum information science and technology.