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arXiv:1409.5039 · International Journal of Quantum Information

Experimental violation of a d-dimensional Bell inequality using energy-time entangled photons

Sacha Schwarz, Bänz Bessire, André Stefanov

Published Nov 1, 2014• 9 citations
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Abstract

We experimentally study the violation of the CGLMP inequality for entangled 2-qubit and 2-qutrit states with different degrees of entanglement using numerically optimized measurement settings. The qudits are encoded and manipulated in the frequency spectrum of broadband energy-time entangled photons by taking into account a spatial light modulator (SLM). The latter allows to discretize the spectrum into bins. By controlling each frequency bin individually, the generation of maximally and non-maximally entangled qutrits is verified through quantum state tomography (QST).

DOI
10.1142/s0219749915600266

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High-dimensional quantum entanglement is drawing attention because it enables us to perform quantum information tasks that are robust against noises. To test the nonlocality of entangled qudits, the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality has been proposed and demonstrated using qudits based on orbital angular momentum, time-energy uncertainty, and frequency bins. Here, we report the generation and observation of time-bin entangled ququarts. We implemented a measurement for the CGLMP inequality test using cascaded delay Mach-Zehnder interferometers fabricated by using planar light-wave circuit technology, with which we achieved a precise and stable measurement for time-bin-entangled ququarts. In addition, we generated an optimized entangled state by modulating the pump pulse intensities, with which we can observe the theoretical maximum violation for the CGLMP inequality test. As a result, we successfully observed a Bell-type parameter ${S}_{4}=2.774\ifmmode\pm\else\textpm\fi{}0.025$ violating the CGLMP inequality for the maximally entangled state and an enhanced Bell-type parameter ${S}_{4}=2.913\ifmmode\pm\else\textpm\fi{}0.023$ for the optimized entangled state.
Entanglement is a key feature of quantum mechanics and is best suited to study the peculiar nature of non-classical correlations. Higher dimensional entangled bipartite systems beyond qubits allow for new insights in generalized Bell inequalities and for enhanced bit rates within protocols for quantum key distribution. Entangled qutrits and ququarts in the time domain have been implemented interferometrically. This paper proposes and demonstrates the capability to encode qudits in the spectrum of energy-time entangled photons by means of spectral amplitude and phase modulation.
We introduce a method of investigating qutrit nonclassicality by translating qutrit operators to symmetric two-qubit operators. We show that this procedure sheds light on the discrepancy between maximal qutrit entanglement and maximal nonclassicality of qutrit correlations. Namely, we express Bell operators corresponding to qutrit Bell inequalities in terms of symmetric two-qubit operators and analyze the maximal quantum violation of a given Bell inequality from the qubit perspective. As an example we show that the two-qutrit Collins-Gisin-Linden-Massar-Popescu (CGLMP) Bell inequality can be seen as a combination of Mermin's and Clauser-Horne-Shimony-Holt CHSH) qubit Bell inequalities, and therefore the optimal state violating this combination differs from the one which corresponds to the maximally entangled state of two qutrits. In addition, we discuss the same problem for a three-qutrit inequality. We also demonstrate that the maximal quantum violation of the CGLMP inequality follows from complementarity of correlations.