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Physical Review A

Time-resolved measurement of Bell inequalities and the coincidence loophole

Mónica Agüero, Alejandro Andrés Hnilo, Marcelo Gregorio Kovalsky

Published Nov 30, 2012• 22 citations
Publisher

Abstract

We report an Einstein-Podolsky-Rosen-Bohm experiment with a pulsed source of entangled pairs of photons, recording the time of arrival of the pulses and of the detection of each single photon. This allows varying the parameters of the analysis (as the size of the time coincidence window) at will after the experiment has ended. Among other results, we present the measurement of the time variation of the Clauser-Horne-Shimony-Holt parameter during the pulse. The obtained results close (or at least impose new and tight restrictions to) the last loophole that remains open in the tests of quantum mechanics vs local realism (the so-called coincidence loophole).

DOI
10.1103/physreva.86.052121

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We report an Einstein-Podolsky-Rosen-Bohm experiment with a pulsed source of entangled pairs of photons, recording the time of arrival of the pulses and of the detection of each single photon. This allows varying the parameters of the analysis (as the size of the time coincidence window) at will after the experiment has ended. Among other results, we present the measurement of the time variation of the Clauser-Horne-Shimony-Holt parameter during the pulse. The obtained results close (or at least impose new and tight restrictions to) the last loophole that remains open in the tests of quantum mechanics vs local realism (the so-called coincidence loophole).
Recent experiments using innovative optical detectors and techniques have strongly increased the capacity of testing the violation of the Bell's inequalities in Nature. Most of them have used the Eberhard's inequality (EI) to close the ``detection'' loophole. Closing the ``locality'' loophole has been attempted by spacelike separated detections and fast changes of the bases of observation, driven by random number generators of new design. Also, pulsed pumping and time-resolved data recording to close the ``time-coincidence'' loophole, and sophisticated statistical methods to close the ``memory'' loophole, have been used. In this paper, the meaning of the EI is reviewed. A simple hidden variables theory based on a relaxation of the condition of ``measurement independence,'' which was devised long ago for the Clauser-Horne-Shimony and Holt inequality, is adapted to the EI case. It is used here to evaluate the significance of the results of the recent experiments, which are briefly described. A table summarizes the main results.
Abstract This chapter presents a detailed discussion of Bell inequalities and their experimental tests. Starting from the Aharonov-Bohm version of the Einstein-Podolsky-Rosen (EPR) paradox, we review EPR’s criteria for realism and completeness and Bell’s locality condition, before deriving the Clauser-Horne-Shimony-Holt (CHSH) inequality. This is followed by an exposition on Bell’s original inequality and other Bell inequalities by Wigner, as well as Clauser and Horne. We then discuss the milestones in the experimental violation of Bell inequalities, from the experiment of Freedman and Clauser in the 1970s, to the efforts of Aspect et al. in the 1980s, the experiments by the teams of Zeilinger and Gisin in the 1990s, and culminating the loophole-free tests in 2015. Finally we turn to a brief discussion of the interpretations of quantum mechanics, focusing on contrasting the realist views held by, e.g., Einstein and Bell, and the informational views with proponents such as Brukner and Zeilinger
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.
In a local realist model, physical properties are defined prior to and independent of measurement and no physical influence can propagate faster than the speed of light. Proper experimental violation of a Bell inequality would show that the world cannot be described with such a model. Experiments intended to demonstrate a violation usually require additional assumptions that make them vulnerable to a number of ``loopholes.'' In both pulsed and continuously pumped photonic experiments, an experimenter needs to identify which detected photons belong to the same pair, giving rise to the coincidence-time loophole. Here, via two different methods, we derive Clauser-Horne- and Eberhard-type inequalities that are not only free of the fair-sampling assumption (thus not being vulnerable to the detection loophole), but also free of the fair-coincidence assumption (thus not being vulnerable to the coincidence-time loophole). Both approaches can be used for pulsed as well as for continuously pumped experiments. Moreover, as they can also be applied to already existing experimental data, we finally show that a recent experiment [Giustina et al., Nature (London) 497, 227 (2013)] violated local realism without requiring the fair-coincidence assumption.