Enhanced violations of Leggett-Garg inequalities in an experimental three-level system

Wang, Kunkun; Emary, Clive; Zhan, Xiang; Bian, Zhihao; Li, Jian; Xue, Peng

doi:10.1364/oe.25.031462

Cited by 31 publications

(20 citation statements)

References 54 publications

(81 reference statements)

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“…(1.2) is −1/2. This is the Lüders bound [40][41][42][43][44] and is the maximal violation possible for projective measurements of a dichotomic variable Q (Lüders measurements) and coincides numerically with the Tsirelson bound [11] in Bell experiments. However, for systems with three or more levels, there are different macrorealistically equivalent methods of measuring the correlators which permit violations of the Lüders bound.…”

Section: B Two-time Nsit Conditions In the Triple Slit Experimentssupporting

confidence: 67%

Leggett-Garg tests for macrorealism: interference experiments and the simple harmonic oscillator

Halliwell,

Bhatnagar,

Ireland

et al. 2020

Preprint

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Leggett-Garg (LG) tests for macrorealism were originally designed to explore quantum coherence on the macroscopic scale. Interference experiments and systems modelled by harmonic oscillators provide useful examples of situations in which macroscopicity has been approached experimentally and may be turned into LG tests with a dichotomic variable Q by simple partitionings of a continuous variable such as position. Applying this approach to the double-slit experiment in which a measurement at the slits and screen are considered, we find that LG violations are always accompanied by destructive interference. The converse is not true in general and we find that there are non-trivial regimes in which there is destructive interference but the two-time LG inequalities are satisfied which implies that it is in fact often possible to assign (indirectly determined) probabilities for the interferometer paths. Similar features have been observed in recent work involving a LG analysis of a Mach-Zehnder interferometer and we compare with those results. We also compare with the related problem in which a more direct determination of the paths is carried out using a variable-strength measurement at the slits and the resulting deterioration of the interference pattern is examined. We extend the analysis to the triple-slit experiment. We find examples of some surprising relationships between LG inequalities and NSIT conditions that do not exist for dichotomic variables, including a violation of the Lüders bound. We analyse a two-time LG inequality for the simple harmonic oscillator. We find an analytically tractable example showing a two-time LG violation with a gaussian initial state, echoing recent results of Bose et al (Phys. Rev. Lett. 120, 210402 (2018)).

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Section: B Two-time Nsit Conditions In the Triple Slit Experimentssupporting

confidence: 67%

Leggett-Garg tests for macrorealism: interference experiments and the simple harmonic oscillator

Halliwell,

Bhatnagar,

Ireland

et al. 2020

Preprint

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“…The two and three-time LG inequalities given above have a lower bound of −1/2 in quantum theory. This is the so-called Lüders bound [35,[37][38][39][40] and is readily derived as follows. Suppose for example we consider the LG2 for times t 2 , t 3 , we have…”

Section: Discussionmentioning

confidence: 99%

“…However, what an experimentalist will measure in a lab is independent of this choice. For measurements of a dichotomic operators, the LGIs, in quantum theory, have a lower bound of − 1 2 , the socalled Lüders bound [35,[37][38][39][40]. Similarly, the 3rd-order…”

Section: 2)mentioning

confidence: 99%

Detecting violations of macrorealism when the original Leggett-Garg inequalities are satisfied

Majidy,

Halliwell,

Laflamme

2021

Preprint

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Macroscopic realism (MR) is the notion that a time-evolving system possesses definite properties, irrespective of past or future measurements. Quantum mechanical theories can, however, produce violations of MR. Most research to date has focused on a single set of conditions for MR, the Leggett-Garg inequalities (LGIs), and on a single data set, the "standard data set", which consists of single-time averages and second-order correlators of a dichotomic variable Q for three times. However, if such conditions are all satisfied, then where is the quantum behaviour? In this paper, we provide an answer to this question by considering expanded data sets obtained from finer-grained measurements and MR conditions on those sets. We consider three different situations in which there are violations of MR that go undetected by the standard LGIs. First, we explore higher-order LGIs on a data set involving third-and fourth-order correlators, using a spin-1/2 and spin-1 system. Second, we explore the pentagon inequalities (PIs) and a data set consisting of all possible averages and second-order correlators for measurements of Q at five times. Third, we explore the LGIs for a trichotomic variable and measurements made with a trichotomic operator to, again, identify violations for a spin-1 system beyond those seen with a single dichotomic variable. We also explore the regimes in which combinations of two and three-time LGIs can be satisfied and violated in a spin-1 system, extending recent work. We discuss the possible experimental implementation of all the above results.

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“…However, MPD utilizes photon-counting intensity detection with a significantly low experimental complexity. It is also simpler compared with the LGI violating architectures utilizing single-photon sources and Mach-Zehnder interferometers [11,20,21]. Besides that, light sources not fully coherent in terms of spatial and temporal dimensions are theoretically modeled while the violation of LGI and QPI are numerically analyzed for specific MPD setup geometry satisfying coherence of light under Gaussian source beam assumptions.…”

Section: Introductionmentioning

confidence: 99%

Theory of Quantum Path Entanglement and Interference with Multiplane Diffraction of Classical Light Sources

Gülbahar

2020

Entropy

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Quantum history states were recently formulated by extending the consistent histories approach of Griffiths to the entangled superposition of evolution paths and were then experimented with Greenberger–Horne–Zeilinger states. Tensor product structure of history-dependent correlations was also recently exploited as a quantum computing resource in simple linear optical setups performing multiplane diffraction (MPD) of fermionic and bosonic particles with remarkable promises. This significantly motivates the definition of quantum histories of MPD as entanglement resources with the inherent capability of generating an exponentially increasing number of Feynman paths through diffraction planes in a scalable manner and experimental low complexity combining the utilization of coherent light sources and photon-counting detection. In this article, quantum temporal correlation and interference among MPD paths are denoted with quantum path entanglement (QPE) and interference (QPI), respectively, as novel quantum resources. Operator theory modeling of QPE and counterintuitive properties of QPI are presented by combining history-based formulations with Feynman’s path integral approach. Leggett–Garg inequality as temporal analog of Bell’s inequality is violated for MPD with all signaling constraints in the ambiguous form recently formulated by Emary. The proposed theory for MPD-based histories is highly promising for exploiting QPE and QPI as important resources for quantum computation and communications in future architectures.

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Enhanced violations of Leggett-Garg inequalities in an experimental three-level system

Cited by 31 publications

References 54 publications

Leggett-Garg tests for macrorealism: interference experiments and the simple harmonic oscillator

Leggett-Garg tests for macrorealism: interference experiments and the simple harmonic oscillator

Detecting violations of macrorealism when the original Leggett-Garg inequalities are satisfied

Theory of Quantum Path Entanglement and Interference with Multiplane Diffraction of Classical Light Sources

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