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arXiv:2507.07904 · EPJ Quantum Technology

Testing time order and Leggett-Garg inequalities with noninvasive measurements on public quantum computers

Tomasz Rybotycki, Tomasz Białecki, Josep Amengual i Batle, Bartłomiej Zglinicki, Adam Szereszewski, Wolfgang Belzig, Adam Bednorz

Published Jan 5, 2026• 0 citations

Abstract

Abstract We demonstrate the first violation of the Leggett-Garg inequality and time-order noninvariance on public quantum computers using genuine noninvasive measurements. By gathering sufficiently large statistics, we have been able to violate Leggett-Garg inequality and time-order invariance. The detailed analysis of the data on 10 qubit sets from 5 devices available on IBM Quantum and one on IonQ reveals violations beyond 5 standard deviations in almost all cases. We implemented our protocols using fractional gates, newly available on the IBM Heron devices, allowing us to benchmark them in application to weak measurements. The noninvasiveness is supported by a qualitative and quantitative agreement with the model of weak disturbance. Moreover, our data expose statistically significant deviations from theoretical predictions that exceed declared device error rates, establishing weak measurement protocols as a sensitive benchmark for quantum hardware. These advances transform public quantum computers into practical testbeds for probing foundational questions of realism and temporal order with unprecedented accessibility and precision.

DOI: 10.1140/epjqt/s40507-025-00457-9

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The Leggett-Garg inequality holds for any macrorealistic system that is being measured noninvasively. A violation of the inequality can signal that a system does not conform to our primal intuition about the physical world. Alternatively, a violation can simply indicate that a ``clumsy'' experimental technique led to invasive measurements. Here, we consider a recent Leggett-Garg test designed to try to rule out the mundane second possibility. We tailor this Leggett-Garg test to the IBM 5Q Quantum Experience system and find compelling evidence that qubit

{Q}_{2}

of the system cannot be described by noninvasive macrorealism.

The Leggett-Garg inequality is a widely used test of the ``quantumness'' of a system and involves correlations between measurements realized at different times. According to its widespread interpretation, a violation of the Leggett-Garg inequality disproves macroscopic realism and noninvasiveness. Nevertheless, recent results point out that macroscopic realism is a model-dependent notion and that one should always be able to attribute to invasiveness a violation of a Leggett-Garg inequality. This opens some natural questions: How do we provide such an attribution in a systematic way? How can apparent macroscopic realism violation be recast into a dimensional-independent invasiveness model? The present work answers these questions by introducing an operational model where the effects of invasiveness are controllable through a parameter associated with what is called the measurability of the physical system. Such a parameter leads to different generalized measurements that can be associated with the dimensionality of a system, to measurement errors, or to back action.