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Chinese Physics Letters

Experimental Violation of Multiple-Measurement Time-Domain Bell's Inequalities

Jian‐Shun Tang, Yulong Li, Chuan‐Feng Li, Jin‐Shi Xu, Geng Chen, Yang Zou, Zong‐Quan Zhou, Guang‐Can Guo

Published Jun 1, 2011• 2 citations
Publisher

Abstract

In the original time-domain Bell's inequalities (Leggett-Garg-type inequalities), the physical objective is measured at three time points. When more time points are chosen, several methods can be used to extend these inequalities. We experimentally demonstrate the violation of these extended inequalities using single photons from a self-assembled quantum dot. In general, for each extension, the quantity by which the quantum-mechanics value exceeds the classical limit becomes larger as the number of measurement time points increases. This quantity has a maximum value for the extensions that have the same number of measurement time points. Furthermore, we evaluate the noise tolerance for these extensions with a quantity that is related to the number of standard deviations by which the experimental result surpasses the classical limit.

DOI
10.1088/0256-307x/28/6/060304

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In the original time-domain Bell's inequalities (Leggett-Garg-type inequalities), the physical objective is measured at three time points. When more time points are chosen, several methods can be used to extend these inequalities. We experimentally demonstrate the violation of these extended inequalities using single photons from a self-assembled quantum dot. In general, for each extension, the quantity by which the quantum-mechanics value exceeds the classical limit becomes larger as the number of measurement time points increases. This quantity has a maximum value for the extensions that have the same number of measurement time points. Furthermore, we evaluate the noise tolerance for these extensions with a quantity that is related to the number of standard deviations by which the experimental result surpasses the classical limit.
Quantum mechanics presents peculiar properties that, on the one hand, have been the subject of several theoretical and experimental studies about its very foundations and, on the other hand, provide tools for developing new technologies, the so-called quantum technologies. The nonclassicality pointed out by Leggett-Garg inequalities has represented, with Bell inequalities, one of the most investigated subjects. In this article we study the connection of Leggett-Garg inequalities with a new emerging field of quantum measurement, the weak values in the case of a series of sequential measurements on a single object. In detail, we perform an experimental study of the four-time-correlator Leggett-Garg test, by exploiting single and sequential weak measurements performed on heralded single photons.
Despite the great success of quantum mechanics, questions regarding its application still exist and the boundary between quantum and classical mechanics remains unclear. Based on the philosophical assumptions of macrorealism and noninvasive measurability, Leggett and Garg devised a series of inequalities (LG inequalities) involving a single system with a set of measurements at different times. Introduced as the Bell inequalities in time, the violation of LG inequalities excludes the hidden-variable description based on the above two assumptions. We experimentally investigated the single photon LG inequalities under decoherence simulated by birefringent media. These generalized LG inequalities test the evolution trajectory of the photon and are shown to be maximally violated in a coherent evolution process. The violation of LG inequalities becomes weaker with the increase of interaction time in the environment. The ability to violate the LG inequalities can be used to set a boundary of the classical realistic description.
Leggett and Garg defined macrorealism by positing that a macroscopic system will exist in a well-defined state at all times, and that this state can be measured without disturbing it. They also formulated a class of inequalities which hold under macrorealism but can be violated by quantum mechanics. The degree to which quantum systems can violate these inequalities is restricted by the temporal Tsirelson bounds. Recently variants of Leggett-Garg inequalities which can be violated to the algebraic maximum 3 for a sufficient large number of measurement times have been proposed. In this work we report an experimental test of quantum violation of the variants of Leggett-Garg inequalities beyond the temporal Tsirelson bounds, up to $2.248\ifmmode\pm\else\textpm\fi{}0.039$ in five-time measurement scenarios for a photonic qubit. Our results clearly show the advantages of the modified measurement scenarios.
Leggett-Garg inequalities are tests of macroscopic realism that can be violated by quantum mechanics. In this letter, we realise photonic Leggett-Garg tests on a three-level system and implement measurements that admit three distinct measurement outcomes, rather than the usual two. In this way we obtain violations of three- and four-time Leggett-Garg inequalities that are significantly in excess of those obtainable in standard Leggett-Garg tests. We also report violations the quantum-witness equality up to the maximum permitted for a three-outcome measurement. Our results highlight differences between spatial and temporal correlations in quantum mechanics.
Leggett-Garg inequalities are tests of macroscopic realism that can be violated by quantum mechanics. In this letter, we realise photonic Leggett-Garg tests on a three-level system and implement measurements that admit three distinct measurement outcomes, rather than the usual two. In this way we obtain violations of three- and four-time Leggett-Garg inequalities that are significantly in excess of those obtainable in standard Leggett-Garg tests. We also report violations the quantum-witness equality up to the maximum permitted for a three-outcome measurement. Our results highlight differences between spatial and temporal correlations in quantum mechanics.
Leggett-Garg's inequalities predict sharp bounds for some classical correlation functions that address the quantum or classical nature of real-time evolutions. We experimentally observe the violations of these bounds on single- and multiqubit systems, in different settings, exploiting the IBM Quantum platform. In the multiqubit case, we introduce the Leggett-Garg-Bell's inequalities as an alternative to the previous ones. Measuring these correlation functions, we find quantum error mitigation to be essential to spot inequalities violations. Accessing only two qubit readouts, we assess Leggett-Garg-Bell's inequalities to emerge as the most efficient quantum coherence witnesses to be used for investigating quantum hardware, among those introduced. Our analysis highlights the limits of current quantum platforms, showing that the above-mentioned correlation functions deviate from theoretical prediction as the number of qubits and the depth of the circuit grow.