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Chinese Physics B

Strong violations of locality by testing Bell’s inequality with improved entangled-photon systems

Yao Wang, Dai-He Fan, Wei-Jie Guo, Lian-Fu Wei

Published Aug 1, 2015• 0 citations
Publisher

Abstract

Bell’s theorem states that quantum mechanics cannot be accounted for by any local theory. One of the examples is the existence of quantum non-locality is essentially violated by the local Bell’s inequality. Therefore, the violation of Bell’s inequality (BI) has been regarded as one of the robust evidences of quantum mechanics. Until now, BI has been tested by many experiments, but the maximal violation (i.e., Cirel’son limit) has never been achieved. By improving the design of entangled sources and optimizing the measurement settings, in this work we report the stronger violations of the Clauser–Horne–Shimony–Holt (CHSH)-type Bell’s inequality. The biggest value of Bell’s function in our experiment reaches to a significant one: S = 2.772± 0.063, approaching to the so-called Cirel’son limit in which the Bell function value is . Further improvement is possible by optimizing the entangled-photon sources.

DOI
10.1088/1674-1056/24/8/084203

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Bell’s theorem states that quantum mechanics cannot be accounted for by any local theory. One of the examples is the existence of quantum non-locality is essentially violated by the local Bell’s inequality. Therefore, the violation of Bell’s inequality (BI) has been regarded as one of the robust evidences of quantum mechanics. Until now, BI has been tested by many experiments, but the maximal violation (i.e., Cirel’son limit) has never been achieved. By improving the design of entangled sources and optimizing the measurement settings, in this work we report the stronger violations of the Clauser–Horne–Shimony–Holt (CHSH)-type Bell’s inequality. The biggest value of Bell’s function in our experiment reaches to a significant one: S = 2.772± 0.063, approaching to the so-called Cirel’son limit in which the Bell function value is . Further improvement is possible by optimizing the entangled-photon sources.
Bell’s inequality plays an important role in quantum mechanics. Many experiments have been made to test the Bell’s inequality by using various bipartite entangled sources. However, the maximal violation of the Bell inequality (i.e., the Cirel’son’s limit) has not been reached yet, due to various practically-existing imperfections (e.g., entangled source is not the pure maximally-entangled state, and the measurement settings used are not the best ones). In this paper, we investigate experimentally an approach to enhance the violation degree of Bell’s inequality with the commercialized entangled photons by optimizing the measurement settings for the experimentally-reconstructed density matrix of the entangled photons. It is shown that the measurement setting related to the pure entangled state can not get maximally violation generally. However, upon the density matrix reconstructed by tomographic technique, optimal measurement settings can be found. With these optimal settings, we consequently found that the violation degree of the Bell’s inequality can be increased. This suggests a possible approach to optimize the test of Bell’s inequality.
Many experiments have been made to test the Clauser–Horne–Shimony–Holt (CHSH)–Bell inequality (CBI). However, the Cirel’son’s limit has not been reached yet, due to various practically existing imperfections. In this paper, we experimentally investigate how to select the measurement settings for obtaining the optimal violation of CBI for a mixed entangled state. With the commercialized entangled source, we first determine the entanglement degree of the generated photon pairs by using the tomographic technique, and then numerically optimize the measurement settings. Finally, we experimentally obtain the optimal violation of the CBI with the present commercialized entangled source without the maximal entanglement.
Cirel'son inequality states that the absolute value of the combination of quantum correlations appearing in the Clauser-Horne-Shimony-Holt (CHSH) inequality is bound by 2 square root of (2). It is shown that the correlations of two qubits belonging to a three-qubit system can violate the CHSH inequality beyond 2 square root of (2). Such a violation is not in conflict with Cirel'son's inequality because it is based on postselected systems. The maximum allowed violation of the CHSH inequality, 4, can be achieved using a Greenberger-Horne-Zeilinger state.
Entanglement, describing the inseparability of a quantum multiparty system, is one of the most intriguing features of quantum mechanics. Violation of Bell inequality, for ruling out the possibility of local hidden variable theories, is commonly used as a strong witness for quantum entanglement. In previous Bell test experiments with photonic entanglement based on two-photon coincidence measurement, the photon temporal wave packets are absorbed completely by the detectors. That is, the photon coherence time is much shorter than the detection time window. Here we demonstrate generation of frequency-bin entangled narrowband biphotons, and for the first time, test the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality |S|<= 2 for their nonlocal temporal correlations with time-resolved detection. We obtain a maximum |S| value of 2.52+/-0.48 that violates the CHSH inequality. Our result will have applications in quantum information processing involving time-frequency entanglement.
Bell's theorem revealed the fundamental incompatibility between the predictions of quantum mechanics and local realism. Bell inequality violations have since demonstrated quantum nonlocality using photons and internal states of massive particles, but never using their motional states. Here we report the first Bell inequality violation in the motional states of massive particles. Using momentum-entangled pairs of metastable helium atoms manipulated by matter-wave interferometry, we measure a Clauser-Horne-Shimony-Holt (CHSH) Bell parameter of S=2.52±0.17S = 2.52 \pm 0.17S=2.52±0.17, violating the CHSH-Bell inequality (S≤2S \le 2S≤2). Our work completes a long-standing objective in quantum atom optics by extending Bell tests from internal quantum variables to the external degrees of freedom of massive particles, opening a new regime for exploring quantum nonlocality in matter waves and for investigating the interplay between quantum mechanics and gravity.
Nonlocality is a fascinating and counterintuitive aspect of nature, revealed by the violation of a Bell inequality. The standard and easiest configuration in which Bell inequalities can be measured has been proposed by Clauser-Horne-Shimony-Holt (CHSH). However, alternative nonlocality tests can also be carried out. In particular, Bell inequalities requiring multiple measurement settings can provide deeper fundamental insights about quantum nonlocality, as well as offering advantages in the presence of noise and detection inefficiency. In this paper we show how these nonlocality tests can be performed using a commercially available source of entangled photon pairs. We report the violation of a series of these nonlocality tests (I3322{I}_{3322}I3322​, I4422{I}_{4422}I4422​, and chained inequalities). With the violation of the chained inequality with 4 settings per side we put an upper limit at 0.49 on the local content of the states prepared by the source (instead of 0.63 attainable with CHSH). We also quantify the amount of true randomness that has been created during our experiment (assuming fair sampling of the detected events).