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Journal of Optics

Realization of Hardy’s thought experiment using classical light

Xiong Zhang, Yifan Sun, Xin-Bing Song, Xiangdong Zhang

Published Aug 11, 2016• 3 citations
Publisher

Abstract

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.

DOI
10.1088/2040-8978/18/9/095604

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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.
We test experimentally the quantum ``paradox'' proposed by L. Hardy [Phys. Rev. Lett. 71, 1665 (1993)] by using single photons instead of photon pairs. This is achieved by addressing two compatible degrees of freedom of the same particle, namely, its spin angular momentum, determined by the photon polarization, and its orbital angular momentum, a property related to the optical transverse mode. Because our experiment involves a single particle, we cannot use locality to logically enforce noncontextuality, which must therefore be assumed based only on the observables' compatibility. On the other hand, our single-particle experiment can be implemented more simply and allows larger detection efficiencies than typical two-particle ones, with a potential future advantage in terms of closing the detection loopholes.
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.
Characterizing high-dimensional entangled states is of crucial importance in quantum information science and technology. Recent theoretical progress has been made to extend Hardy's paradox into a general scenario with multisetting and multidimensional systems, which enables the maximum probability of nonlocal events to surpass the bound that was limited in Hardy's original test. Hitherto, no experimental verification has been conducted to verify Hardy's paradox, as most of the previous experimental efforts were restricted to two-dimensional systems. Here, based on two-photon high-dimensional orbital angular momentum (OAM) entanglement, we report an experiment to demonstrate Hardy's paradox for multiple settings and multiple outcomes. We demonstrate the paradox for two-setting higher-dimensional OAM subspaces up to d=7d=7d=7, which reveals that the nonlocal events increase with dimension. Furthermore, we showcase the nonlocality with an experimentally recorded probability of 36.77% for a five-setting three-dimensional OAM subspace via entanglement concentration, thus showing a sharper contradiction between quantum mechanics and classical theory.
We report the first experimental realization of classical hypercorrelation, correlated simultaneously in every degree of freedom (DOF), from observing a Bell-type inequality violation in each DOF: polarization and orbital angular momentum (OAM). Based on such a classical hypercorrelation, we have realized the analogy of quantum superdense coding in classical optics. Comparing it with quantum superdense coding using pairs of photons simultaneously entangled in polarization and OAM, we find that it exhibits many advantages. It is not only very convenient to realize in classical optics, the attainable channel capacity in the experiment for such a superdense coding can also reach 3 bits, which is higher than that (2.8 bits) of usual quantum one. Our findings can not only give novel insight into quantum physics, they may also open a new field of applications in the classical optical information process.
Hardy's nonlocality proof is considered as "the best version of Bell's theorem". We report an experimental implementation of this by measuring the orbital angular momentum (OAM) of entangled twisted photon pairs. Two advantages arise from using twisted photons. First, the limited OAM spectrum generated by parametric down-conversion provides a natural set of OAM non-maximally entangled states with selective degrees of entanglement. Second, the measurement of any non-trivial superposition of OAM states can be conveniently done with spatial light modulators. We measure states that are defined on asymmetric OAM Bloch spheres and show results which are incompatible with local realism.