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Quantum Science and Technology

CHSH inequality test via disturbance-free measurement

Sang Min Lee, Min-Su Kim, Heonoh Kim, Han Seb Moon, Sang Wook Kim

Published Jul 3, 2018• 7 citations
Publisher

Abstract

Abstract We propose disturbance-free measurement (DFM) using a ‘weak-value’ scheme, in which a weakly measured quantum system is post-selected (to the initial state) to confirm that there is no disturbance. The probability of obtaining the non-disturbed state is asymptotically close to unity. We theoretically show that outcomes of the DFM for a two-qubit state satisfy the Clauser–Horne–Shimony–Holt inequality. We experimentally demonstrate the test for a typical (maximally entangled) two-qubit state based on a linear optical system. In experiments, polarization-entangled photon-pairs generated by the spontaneous parametric down-conversion process are measured by instruments such as strength-variable polarization-measurement apparatuses and a fiber-based Bell-state analyzer.

DOI
10.1088/2058-9565/aad0cc

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Microwave and Optical Technology Letters•Aug 24, 2012•2 citations
Abstract We propose disturbance-free measurement (DFM) using a ‘weak-value’ scheme, in which a weakly measured quantum system is post-selected (to the initial state) to confirm that there is no disturbance. The probability of obtaining the non-disturbed state is asymptotically close to unity. We theoretically show that outcomes of the DFM for a two-qubit state satisfy the Clauser–Horne–Shimony–Holt inequality. We experimentally demonstrate the test for a typical (maximally entangled) two-qubit state based on a linear optical system. In experiments, polarization-entangled photon-pairs generated by the spontaneous parametric down-conversion process are measured by instruments such as strength-variable polarization-measurement apparatuses and a fiber-based Bell-state analyzer.
We propose disturbance-free measurement using a "weak-value" scheme, in which a weakly measured quantum system is post-selected (to the initial state) to confirm that there is no disturbance. The probability of obtaining the non-disturbed state is asymptotically close to unity. We theoretically show that outcomes of the disturbance-free measurement for a two-qubit state satisfy the Clauser--Horne--Shimony--Holt inequality. We experimentally demonstrate the test for a typical (maximally entangled) two-qubit state based on a linear optical system. In experiments, polarization-entangled photon-pairs generated by the spontaneous parametric down-conversion process are measured by instruments such as strength-variable polarization-measurement apparatuses and a fiber-based Bell state analyzer.
We propose an asymptotic disturbance-free measurement using the so-called weak-value scheme,where the weakly measured quantum system is measured for a second time, to confirm that it is disturbance-free; moreover, the probability of obtaining the non-disturbed state must approach one. We show that the weak-measurement outcomes of the Bell state post-selected in this manner exhibit classical behavior in the sense that they satisfy the Clauser-Horne-Shimony-Holt inequality. However, the inequality is violated if all outcomes without post-selection are considered. We experimentally confirm our idea by performing joint weak measurement of polarization-entangled photon-pairs and subsequent fiber-based Bell-state measurement.
We theoretically and experimentally investigate the optimal conditions for the Bell experiment using spontaneous parametric down-conversion (SPDC) sources. In theory, we show that a relatively large average photon number (typically $\ensuremath{\sim}0.5$) is desirable to observe the maximum violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality. Moreover, we show that the violation converges to 0.27 in the limit of large average photon number. In experiment, we perform the Bell experiment without postselection using polarization-entangled photon pairs at 1550-nm telecommunication wavelength generated from SPDC sources. While the violation of the CHSH inequality is not directly observed due to the overall detection efficiencies of our system, the experimental values agree well with those obtained by the theory with experimental imperfections. Furthermore, in the range of small average photon numbers ($\ensuremath{\le}0.1$), we propose and demonstrate a method to estimate the ideal CHSH value intrinsically contained in the tested state from the lossy experimental data without assuming the input quantum state.
Abstract The Clauser–Horne–Shimony–Holt (CHSH) inequality test is widely used as a mean of invalidating the local deterministic theories. Most attempts to experimentally test nonlocality have presumed unphysical idealizations that do not hold in real experiments, namely, noiseless measurements. We demonstrate an experimental violation of the CHSH inequality that is free of idealization and rules out local models with high confidence. We show that the CHSH inequality can always be violated for any nonzero noise parameter of the measurement. Intriguingly, less entanglement exhibits more nonlocality in the CHSH test with noisy measurements. Furthermore, we theoretically propose and experimentally demonstrate how the CHSH test with noisy measurements can be used to detect weak entanglement on two-qubit states. Our results offer a deeper insight into the relation between entanglement and nonlocality.
A violation of Bell's inequalities using quantum entanglement indicates the nonlocality of two particles such as photons and electrons. We observe a violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality, a particular Bell's inequality, in polarization-entangled photon pairs in the 1550 nm band. For photon pair generation based on spontaneous parametric down conversion, a fiber-optic two-photon interferometer with two periodically poled lithium niobate waveguides is adopted. The obtained S value of the CHSH inequality is 2.44 ±0.02 without subtraction of accidental coincidences, yielding a violation by ∼22 standard deviations in an hour. Two-photon interference with a visibility of 0.885 is also observed. If those coincidences are subtracted, the visibility becomes almost unity.
Abstract In addition to Bell's original inequality, John Clauser, Michael Horne, Abner Shimony, and Richard Holt (CHSH) developed a special form of Bell's inequality which gives classical limits to the expected correlation between two particles. We present a theoretical demonstration of the maximum value for violation of CHSH inequality, S = 2 2\sqrt{2}2​ , for the pure entangled quantum state. Using the spontaneous four‐wave mixing process, we generate polarization‐entangled photon pairs in a highly nonlinear fiber (HNLF) loop, for experimental verification. Using a nonentangled quantum state, we show theoretically that the violation of CHSH inequality is only a property of entangled states. We also show the theoretical solution of violation of the CHSH inequality for a general Greenberger–Horne–Zeilinger state and for an arbitrary state of two particles. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 54:2454–2461, 2012; View this article online at wileyonlinelibrary. com. DOI 10.1002/mop.27127