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Experimental Violation of Bell Inequalities for Systems of over 4000 Dimensions

Hsin-Pin Lo, Che‐Ming Li, Atsushi Yabushita, Yueh-Nan Chen, Chih‐Wei Luo, Takayoshi Kobayashi

Published Jan 26, 2015• 0 citations
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Abstract

Quantum correlations between spatially separated parts of a $d$-dimensional bipartite system ($d\geq 2$) have no classical analog. Such correlations, also called entanglements, are not only conceptually important, but also have a profound impact on information science. In theory the violation of Bell inequalities based on local realistic theories for $d$-dimensional systems provides evidence of quantum nonlocality. Experimental verification is required to confirm whether a quantum system of extremely large dimension can possess this feature, however it has never been performed for large dimension (e.g., $d\geq 1000$). Here, we report that Bell inequalities are experimentally violated for bipartite quantum systems of extremely high dimensionality with the usual ensembles of polarization-entangled photon pairs. Our entanglement source violates Bell inequalities for extremely high dimensionality of $d>4000$. The designed scenario offers a possible new method to investigate the entanglement of multipartite systems of large dimensionality and their application in quantum information processing.

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Quantum correlations between spatially separated parts of a ddd-dimensional bipartite system (d≥2d\geq 2d≥2) have no classical analog. Such correlations, also called entanglements, are not only conceptually important, but also have a profound impact on information science. In theory the violation of Bell inequalities based on local realistic theories for ddd-dimensional systems provides evidence of quantum nonlocality. Experimental verification is required to confirm whether a quantum system of extremely large dimension can possess this feature, however it has never been performed for large dimension (e.g., d≥1000d\geq 1000d≥1000). Here, we report that Bell inequalities are experimentally violated for bipartite quantum systems of extremely high dimensionality with the usual ensembles of polarization-entangled photon pairs. Our entanglement source violates Bell inequalities for extremely high dimensionality of d>4000d>4000d>4000. The designed scenario offers a possible new method to investigate the entanglement of multipartite systems of large dimensionality and their application in quantum information processing.
Quantum correlations between spatially separated parts of a d-dimensional bipartite system (d ≥ 2) have no classical analog. Such correlations, also called entanglements, are not only conceptually important, but also have a profound impact on information science. In theory the violation of Bell inequalities based on local realistic theories for d-dimensional systems provides evidence of quantum nonlocality. Experimental verification is required to confirm whether a quantum system of extremely large dimension can possess this feature, however it has never been performed for large dimension. Here, we report that Bell inequalities are experimentally violated for bipartite quantum systems of dimensionality d = 16 with the usual ensembles of polarization-entangled photon pairs. We also estimate that our entanglement source violates Bell inequalities for extremely high dimensionality of d > 4000. The designed scenario offers a possible new method to investigate the entanglement of multipartite systems of large dimensionality and their application in quantum information processing.
Quantum correlations resulting in violations of Bell inequalities have generated a lot of interest in quantum information science and fundamental physics. In this paper, we address some questions that become relevant in Bell-type tests involving systems with local dimension greater than 2. For CHSH-Bell tests within 2D subspaces of such high-dimensional systems, it has been suggested that experimental violation of Tsirelson's bound indicates that more than 2D entanglement was present. We explain that the overstepping of Tsirelson's bound is due to violation of fair sampling, and can in general be reproduced by a separable state, if fair sampling is violated. For a class of Bell-type inequalities generalized to d-dimensional systems, we then consider what level of violation is required to guarantee d-dimensional entanglement of the tested state, when fair sampling is satisfied. We find that this can be used as an experimentally feasible test of d-dimensional entanglement for up to quite high values of d.
It is theoretically and experimentally shown that photons emitted by statistically independent incoherent classical light sources and measured in the far field in spatially separated modes may display spatial correlations akin to path-entanglement of photons produced by quantum sources. By measuring higher order photon-correlations at different locations, i.e., mmm photons in one mode and one photon in another mode, we experimentally demonstrate for m≥6m \geq 6m≥6 a violation of Bell-type inequalities for spatial degrees of freedom. The spatial correlations among the photons can be understood from state projection where the detection of the first mmm photons projects the sources onto a state which emits the subsequent photon in a strongly correlated manner. From this perspective the entanglement and violation of Bell's inequalities appears as a consequence of nonvanishing cross correlations between noncommuting quadrature phase components of the two spatially separated fields after mmm photons have been recorded. In this way we show that classical systems may produce spatial field correlations violating local realistic theories.
Quantum entanglement is the ability of joint quantum systems to possess global properties (correlation among systems) even when subsystems have no definite individual property. Whilst the 2-dimensional (qubit) case is well-understood, currently, tools to characterise entanglement in high dimensions are limited. We experimentally demonstrate a new procedure for entanglement certification that is suitable for large systems, based entirely on information-theoretics. It scales more efficiently than Bell's inequality and entanglement witness. The method we developed works for arbitrarily large system dimension d and employs only two local measurements of complementary properties. This procedure can also certify whether the system is maximally entangled. We illustrate the protocol for families of bipartite states of qudits with dimension up to 32 composed of polarisation-entangled photon pairs.
Quantum entanglement is the ability of joint quantum systems to possess global properties (correlation among systems) even when subsystems have no definite individual property. Whilst the 2-dimensional (qubit) case is well-understood, currently, tools to characterise entanglement in high dimensions are limited. We experimentally demonstrate a new procedure for entanglement certification that is suitable for large systems, based entirely on information-theoretics. It scales more efficiently than Bell's inequality and entanglement witness. The method we developed works for arbitrarily large system dimension d and employs only two local measurements of complementary properties. This procedure can also certify whether the system is maximally entangled. We illustrate the protocol for families of bipartite states of qudits with dimension up to 32 composed of polarisation-entangled photon pairs.
Bell inequality testing, a well-established method to demonstrate quantum non-locality between remote two-partite entangled systems, is playing an important role in the field of quantum information. The extension to high-dimensional entangled systems, using the so-called Bell-CGLMP inequality, points the way in measuring joint probabilities, the kernel block to construct high dimensional Bell inequalities. Here we show that in theory the joint probability of a two-partite system entangled in a Hilbert space can be measured by choosing a set of basis vectors in its dual space that are related by a Fourier transformation. We next propose an experimental scheme to generate a high-dimensional position-entangled two-photon state aided by a combination of a multiple-slit and a 4 f system, and describe a method to test Bell's inequality using correlated diffraction. Finally, we discuss in detail consequences of such Bell-test violations and experimental requirements.