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arXiv:1502.02811 · Scientific Reports

Bell’s measure and implementing quantum Fourier transform with orbital angular momentum of classical light

Xin-Bing Song, Yifan Sun, Pengyun Li, Hongwei Qin, Xiangdong Zhang

Published Sep 15, 2015• 36 citations
arXivHTMLPDF

Abstract

We perform Bell's measurement for the non-separable correlation between polarization and orbital angular momentum from the same classical vortex beam. The violation of Bell's inequality for such a non-separable classical correlation has been demonstrated experimentally. Based on the classical vortex beam and non-quantum entanglement between the polarization and the orbital angular momentum, the Hadamard gates and conditional phase gates have been designed. Furthermore, a quantum Fourier transform has been implemented experimentally.

DOI
10.1038/srep14113

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We perform Bell's measurement for the non-separable correlation between polarization and orbital angular momentum from the same classical vortex beam. The violation of Bell's inequality for such a non-separable classical correlation has been demonstrated experimentally. Based on the classical vortex beam and non-quantum entanglement between the polarization and the orbital angular momentum, the Hadamard gates and conditional phase gates have been designed. Furthermore, a quantum Fourier transform has been implemented experimentally.
Entanglement in higher dimensions is an attractive concept that is a chal- lenge to realise experimentally. To this end, the entanglement of the orbital angular momentum (OAM) of photons holds promise. The OAM state-space is discrete and theoretically unbounded. In the work that follows, we investi- gate various aspects of OAM entanglement. We show how the correlations in OAM and its conjugate variable, angular position, are determined by phase- matching and the shape of the pump beam in spontaneous parametric down- conversion. We implement tests of quantum mechanics which have been previously done for other variables. We show the Einstein-Podolsky-Rosen paradox for OAM and angle, supporting the incompatibility of quantum me- chanics with locality and realism. We demonstrate violations of Bell-type inequalities, thereby discounting local hidden variables for describing the correlations we observe. We show the Hardy paradox using OAM, again highlighting the nonlocal nature of quantum mechanics. We demonstrate violations of Leggett-type inequalities, thereby discounting nonlocal hidden variables for describing correlations. Lastly, we have looked into the entan- glement of topological vortex structures formed from a special superposition of OAM modes and show violations of Bell-type inequalities confined to a finite, isolated volume.
Optical beams with topological singularities have a Schmidt decomposition.Hence, they display features typically associated with bipartite quantum systems; in particular, these classical beams can exhibit entanglement.This classical entanglement can be quantified by a Bell inequality formulated in terms of Wigner functions.We experimentally demonstrate the violation of this inequality for Laguerre-Gauss (LG) beams and confirm that the violation increases with increasing orbital angular momentum.Our experimental scheme, which is designed to give directly the parity of the Wigner function, yields negativity at the origin for LG 10 beams, whereas for LG 20 we always get a positive value.
Introduction In this chapter, we will be concerned with entangled states of light. Historically, quantum states of light, i.e., photons, have played a dominant role in the experimental study of quantum entanglement. For instance, the first Bell tests and the first realizations of quantum teleportation were performed using two-dimensional polarization-entangled twophoton states [3]. From an experimental point of view these states are readily prepared and manipulated using conventional polarization optics. Recently, however, both theoretical and experimental efforts have shifted towards entanglement in more than two modes , which is often referred to as high-dimensional entanglement. This is much richer than two-dimensional entanglement, as is, for instance, reflected in stronger violations of various measures of nonlocality which reveal the complexity of high-dimensional Hilbert spaces [4–7]. Also, from an applications perspective, it promises a larger channel capacity [8, 9] and improved security for quantum communication [10, 11]. There are several ways to implement high-dimensional two-photon entanglement. One can exploit the temporal [12], frequency [13], or spatial [14–18] degrees of freedom of the optical field. A promising way to implement high-dimensional two-photon entanglement is to use the orbital-angular-momentum (OAM) degree of freedom of light. Light beams that carry OAM have a helical wavefront that spirals around the optical axis during propagation [19]. The winding number m , which characterizes the OAM eigenmodes, can adopt any integer value between −∞ and ∞; since all coaxial OAM modes are orthogonal they can thus span a very high-dimensional Hilbert space.
Hybrid entangled states exhibit entanglement between different degrees of freedom of a particle pair and thus could be useful for asymmetric optical quantum network where the communication channels are characterized by different properties. We report the first experimental realization of hybrid polarization-orbital angular momentum (OAM) entangled states by adopting a spontaneous parametric down conversion source of polarization entangled states and a polarization-OAM transferrer. The generated quantum states have been characterized through quantum state tomography. Finally, the violation of Bell's inequalities with the hybrid two photon system has been observed.
Orbital angular momentum entangled photons emitted by a down-conversion source are shown to be in higher dimensional entangled states. This is experimentally confirmed by demonstrating a violation of Clauser-Horne-Shimony-Holt-type Bell inequalities. The experiment is performed in two steps. First, the two-photon two-dimensional entanglement is demonstrated for orbital angular momentum states by violating the usual CHSH Bell inequality. In a second step the setup is extended in order to show that the entanglement also holds in three dimensions. By using a generalized type of the CHSH Bell inequality, a violation of more than 18 standard deviations is achieved. Higher dimensional entangled states thus allow the realization of new types of quantum communication protocols. They also provide a more secure quantum cryptography scheme.
Abstract We report the realization of Hardy’s thought experiment in classical optical systems. Two different classical optical experiments are implemented. One is based on orbital angular momentum and polarization correlation in a classical optical beam, and the other is based on non-local classical correlation from two separated classical optical beams. All experimental results show that they are analogous to Hardy’s paradox experiments. This means that Hardy’s non-locality proof without inequalities, which is usually used in a quantum system, can also be achieved in classical optical systems.