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Bulletin of the American Physical Society

Experimental violation of a Bell-Leggett-Garg inequality using weak measurements, Part I: Avoiding loopholes

Justin Dressel, T. White, J. Mutus, R. Barends, A. Megrant, Evan R. Jeffrey, D. Sank, J. Kelly, B. Campbell, Y. Chen, Z. Chen, Benjamin Chiaro, A. Dunsworth, I.-C. Hoi, C. Neill, P. J. J. O’Malley, P. Roushan, Chris Quintana, A. Vainsencher, J. Wenner, Austin G. Fowler, Alexander N. Korotkov, A.N. Cleland, John M. Martinis

Published Mar 5, 2015• 0 citations
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By combining the postulates of macrorealism with Bell locality, we derive a qualitatively different hybrid inequality that avoids two loopholes that commonly appear in Leggett-Garg and Bell inequalities. First, locally invasive measurements can be used, which avoids the ``clumsiness'' Leggett-Garg inequality loophole. Second, a single experimental ensemble with fixed analyzer settings is sampled, which avoids the ``disjoint sampling'' Bell inequality loophole. The derived hybrid inequality has the same form as the Clauser-Horne-Shimony-Holt Bell inequality; however, its quantum violation intriguingly requires weak measurements. A realistic explanation of an observed violation requires either the failure of Bell locality or a preparation conspiracy of finely tuned and nonlocally correlated noise. Modern superconducting and optical systems are poised to implement this test.
In contrast to the spatial Bell's inequalities which probe entanglement between spatially separated systems, the Leggett–Garg inequalities test the correlations of a single system measured at different times. Violation of a genuine Leggett–Garg test implies either the absence of a realistic description of the system or the impossibility of measuring the system without disturbing it. Quantum mechanics violates the inequalities on both accounts and the original motivation for these inequalities was as a test for quantum coherence in macroscopic systems. The last few years has seen a number of experimental tests and violations of these inequalities in a variety of microscopic systems such as superconducting qubits, nuclear spins, and photons. In this article, we provide an introduction to the Leggett–Garg inequalities and review these latest experimental developments. We discuss important topics such as the significance of the non-invasive measurability assumption, the clumsiness loophole, and the role of weak measurements. Also covered are some recent theoretical proposals for the application of Leggett–Garg inequalities in quantum transport, quantum biology and nano-mechanical systems.