Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2605.12126

Leggett--Garg Tests in Neural Dynamics: Probing Non-Diffusive Stochastic Structure in Single Neurons

Partha Ghose

quant-phSubmitted May 12, 2026• Announced May 13, 2026• 0 citations
v1 · May 12, 2026v2 · Oct 28, 2026
arXivHTMLPDF

Abstract

We propose an experimental programme to test Leggett--Garg-type temporal correlations in single-neuron dynamics. The goal is to distinguish between diffusive (Wiener/cable-equation) models and non-diffusive persistent stochastic models based on Kac-type finite-velocity processes leading to the Telegrapher's equation. We show that while purely diffusive dynamics satisfies Leggett--Garg inequalities, persistent stochastic dynamics can produce oscillatory temporal correlations capable of violating these inequalities. The Leggett--Garg inequality may be viewed as a temporal analogue of Bell-type constraints. In the present context, however, violation is interpreted conservatively not as evidence of microscopic quantum coherence, but as evidence against a simple trajectory-based diffusive description. The resulting temporal correlations indicate persistence, memory, and contextual temporal structure mathematically analogous to that encountered in quantum systems. Using the analytic continuation connecting Kac processes to Dirac-like envelope equations, we argue that finite-velocity persistent stochastic transport provides a natural mechanism for such non-diffusive temporal correlations. These tests therefore offer a possible experimental probe of contextual and non-Markovian structure in neural dynamics without requiring claims of microscopic quantum coherence in the brain.

Comments
11 pages, no figures

Related papers

Leggett–Garg inequalities

Clive Emary, Neill Lambert, Franco Nori

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.

arXiv:1304.5133•Reports on Progress in Physics•Dec 23, 2013•432 citations

Testing Leggett–Garg inequality using Rydberg superatom

De-Sheng Xiang, Ren Liao, Biao Xu +14 more

Quantum mechanics predicts that measurement is inherently invasive, challenging the macrorealist view that physical properties exist independently of observation. The Leggett–Garg inequality (LGI) provides a test of this worldview, but its violation in systems in collective systems is often challenging due to technical measurement disturbance. By embedding an Elitzur–Vaidman interaction-free measurement (“quantum bomb-testing”) protocol into a microwave-driven Rydberg superatom (a mesoscopically coherent collective system) interferometer—we realize a high-fidelity, sequential measurement test. We observe a clear LGI violation that exceeds the classical bound by nearly 50 standard deviations in such a mesoscopic collective system. This result demonstrates the failure of noninvasive measurability for a collective quantum observable, establishing a scalable platform for probing temporal quantum correlations beyond the single-particle limit.

Advanced Photonics•Sep 11, 2026•0 citations

Leggett-Garg tests for macrorealism in the quantum harmonic oscillator and more general bound systems

C. Mawby, J. J. Halliwell

The Leggett-Garg (LG) inequalities were introduced to test for the possible presence of macroscopic quantum coherence. Since such effects may be found in various types of macroscopic oscillators, we consider the application of the LG approach to the one-dimensional quantum harmonic oscillator and also to more general bound systems, using a single dichotomic variable $Q$ given by the sign of the oscillator position. We present a simple method to calculate the temporal correlation functions appearing in the LG inequalities for any bound system for which the eigenspectrum is (exactly or numerically) known. We apply this result to the quantum harmonic oscillator for a variety of experimentally accessible states, namely, energy eigenstates, and superpositions thereof. For the subspace of states spanned by only the ground state and first excited state, we readily find substantial regions of parameter space in which the LG inequalities at two, three, and four times can each be independently violated or satisfied. We also find that the violations persist, although are reduced, when the sign function defining $Q$ is smeared to reflect experimental imprecision. For higher-energy eigenstates, we find that LG violations diminish, showing the expected classicalization. With a $Q$ defined using a more general type of position coarse graining, we find two-time LG violations even in the ground state. We also show that two-time LG violations in a Gaussian state are readily found if the dichotomic variable at one of the times is taken to be the parity operator. To demonstrate the versatility of the approach, we repeat much of the LG analysis for the Morse potential, finding qualitatively similar physical results.

arXiv:2109.03118•Physical Review A•Feb 28, 2022•10 citations

Addressing the Clumsiness Loophole in a Leggett-Garg Test of Macrorealism

Mark M. Wilde, Ari Mizel

The rise of quantum information theory has lent new relevance to experimental tests for non-classicality, particularly in controversial cases such as adiabatic quantum computing superconducting circuits. The Leggett-Garg inequality is a "Bell inequality in time" designed to indicate whether a single quantum system behaves in a macrorealistic fashion. Unfortunately, a violation of the inequality can only show that the system is either (i) non-macrorealistic or (ii) macrorealistic but subjected to a measurement technique that happens to disturb the system. The "clumsiness" loophole (ii) provides reliable refuge for the stubborn macrorealist, who can invoke it to brand recent experimental and theoretical work on the Leggett-Garg test inconclusive. Here, we present a revised Leggett-Garg protocol that permits one to conclude that a system is either (i) non-macrorealistic or (ii) macrorealistic but with the property that two seemingly non-invasive measurements can somehow collude and strongly disturb the system. By providing an explicit check of the invasiveness of the measurements, the protocol replaces the clumsiness loophole with a significantly smaller "collusion" loophole. © 2011 Springer Science+Business Media, LLC.

Civil War Book Review•Feb 1, 2012•60 citations

Legget-Garg inequality for a quantum model of ion channels

Paulina Trybek, Łukasz Machura, Jerzy Dajka

Temporal quantum correlations, revealed by violations of the Leggett-Garg inequalities (LGIs), offer a powerful framework to probe nonclassical dynamics in conceptual models, including those inspired by the living systems. Here, we examine a three-state representation of ionic transport through the selectivity filter, previously presented by Seifi et al. Using this model, we systematically investigate how different scenarios, such as initial state preparation, the specification of measurement basis, hopping dynamics, and environmental fluctuations, affect the emergence of temporal nonclassicality. The choice of measurement basis is found to play a decisive role in shaping temporal quantum correlations. Our analysis reveals that the strongest LGI violations occur for intermediate model configurations, which represent a short-lived state where a potassium ion is poised for release while still coupled to surrounding water sites, whereas entry and exit configurations exhibit weaker quantum signatures. Static fluctuations of the hopping parameters confine LGI violations to shorter time windows, while dynamic decoherence suppresses them irrespective of the hopping amplitude. Overall, our findings demonstrate that LGI-based analyses can identify stages where temporal quantum correlations are most significant, highlighting the intermediate knock-on configuration as a promising target for future studies of intrinsically quantum effects in ion-conduction phenomena.

Scientific Reports•Jun 18, 2026•0 citations

Violations of the Leggett-Garg inequality in Hybrid Liouvillian Dynamics: The Nonlinear Role of Detector Efficiency

Sourav Paul, Parveen Kumar, Sourin Das

Violations of the Leggett-Garg inequality (LGI) up to its algebraic bound under non-Hermitian dynamics are well established theoretically. Here, we demonstrate that such extreme violations are intrinsically fragile when realistic measurement processes are taken into account. We consider an open two-level system described by a time-local hybrid Liouvillian, with a continuous parameter $q \in [0,1]$, representing detector efficiency, i.e., the fraction of quantum jump trajectories that are retained in the ensemble. This parameter interpolates between trace-preserving Lindblad dynamics ($q=1$) and non-Hermitian ``no-jump" evolution ($q=0$). While $K_3$ approaches its algebraic maximum of 3 in the null-efficiency limit, even an infinitesimal increase in detector efficiency induces a rapid, highly nonlinear suppression toward the classical bound. This logarithmic sensitivity reveals that maximal LGI violations are not robust physical features but rather singular limits of idealized measurement conditions. Our results have direct experimental implications: achieving algebraic LGI violations in systems undergoing continuous time evolution requires near-perfect suppression of detected quantum jumps (i.e., effective post-selection), placing stringent constraints on detector performance. In contrast to discrete protocols based on time-non-divisible dynamics, our framework shows that extreme violations arising within continuous, divisible quantum trajectory evolution constitute a fundamentally fragile regime.

quant-pharXiv:2605.13494•May 14, 2026•0 citations
We propose an experimental programme to test Leggett--Garg-type temporal correlations in single-neuron dynamics. The goal is to distinguish between diffusive (Wiener/cable-equation) models and non-diffusive persistent stochastic models based on Kac-type finite-velocity processes leading to the Telegrapher's equation. We show that while purely diffusive dynamics satisfies Leggett--Garg inequalities, persistent stochastic dynamics can produce oscillatory temporal correlations capable of violating these inequalities.
The Leggett--Garg inequality may be viewed as a temporal analogue of Bell-type constraints. In the present context, however, violation is interpreted conservatively not as evidence of microscopic quantum coherence, but as evidence against a simple trajectory-based diffusive description. The resulting temporal correlations indicate persistence, memory, and contextual temporal structure mathematically analogous to that encountered in quantum systems.
Using the analytic continuation connecting Kac processes to Dirac-like envelope equations, we argue that finite-velocity persistent stochastic transport provides a natural mechanism for such non-diffusive temporal correlations. These tests therefore offer a possible experimental probe of contextual and non-Markovian structure in neural dynamics without requiring claims of microscopic quantum coherence in the brain.
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.
Quantum mechanics predicts that measurement is inherently invasive, challenging the macrorealist view that physical properties exist independently of observation. The Leggett–Garg inequality (LGI) provides a test of this worldview, but its violation in systems in collective systems is often challenging due to technical measurement disturbance. By embedding an Elitzur–Vaidman interaction-free measurement (“quantum bomb-testing”) protocol into a microwave-driven Rydberg superatom (a mesoscopically coherent collective system) interferometer—we realize a high-fidelity, sequential measurement test. We observe a clear LGI violation that exceeds the classical bound by nearly 50 standard deviations in such a mesoscopic collective system. This result demonstrates the failure of noninvasive measurability for a collective quantum observable, establishing a scalable platform for probing temporal quantum correlations beyond the single-particle limit.
The Leggett-Garg (LG) inequalities were introduced to test for the possible presence of macroscopic quantum coherence. Since such effects may be found in various types of macroscopic oscillators, we consider the application of the LG approach to the one-dimensional quantum harmonic oscillator and also to more general bound systems, using a single dichotomic variable QQQ given by the sign of the oscillator position. We present a simple method to calculate the temporal correlation functions appearing in the LG inequalities for any bound system for which the eigenspectrum is (exactly or numerically) known. We apply this result to the quantum harmonic oscillator for a variety of experimentally accessible states, namely, energy eigenstates, and superpositions thereof. For the subspace of states spanned by only the ground state and first excited state, we readily find substantial regions of parameter space in which the LG inequalities at two, three, and four times can each be independently violated or satisfied. We also find that the violations persist, although are reduced, when the sign function defining QQQ is smeared to reflect experimental imprecision. For higher-energy eigenstates, we find that LG violations diminish, showing the expected classicalization. With a QQQ defined using a more general type of position coarse graining, we find two-time LG violations even in the ground state. We also show that two-time LG violations in a Gaussian state are readily found if the dichotomic variable at one of the times is taken to be the parity operator. To demonstrate the versatility of the approach, we repeat much of the LG analysis for the Morse potential, finding qualitatively similar physical results.
The rise of quantum information theory has lent new relevance to experimental tests for non-classicality, particularly in controversial cases such as adiabatic quantum computing superconducting circuits. The Leggett-Garg inequality is a "Bell inequality in time" designed to indicate whether a single quantum system behaves in a macrorealistic fashion. Unfortunately, a violation of the inequality can only show that the system is either (i) non-macrorealistic or (ii) macrorealistic but subjected to a measurement technique that happens to disturb the system. The "clumsiness" loophole (ii) provides reliable refuge for the stubborn macrorealist, who can invoke it to brand recent experimental and theoretical work on the Leggett-Garg test inconclusive. Here, we present a revised Leggett-Garg protocol that permits one to conclude that a system is either (i) non-macrorealistic or (ii) macrorealistic but with the property that two seemingly non-invasive measurements can somehow collude and strongly disturb the system. By providing an explicit check of the invasiveness of the measurements, the protocol replaces the clumsiness loophole with a significantly smaller "collusion" loophole. © 2011 Springer Science+Business Media, LLC.
Temporal quantum correlations, revealed by violations of the Leggett-Garg inequalities (LGIs), offer a powerful framework to probe nonclassical dynamics in conceptual models, including those inspired by the living systems. Here, we examine a three-state representation of ionic transport through the selectivity filter, previously presented by Seifi et al. Using this model, we systematically investigate how different scenarios, such as initial state preparation, the specification of measurement basis, hopping dynamics, and environmental fluctuations, affect the emergence of temporal nonclassicality. The choice of measurement basis is found to play a decisive role in shaping temporal quantum correlations. Our analysis reveals that the strongest LGI violations occur for intermediate model configurations, which represent a short-lived state where a potassium ion is poised for release while still coupled to surrounding water sites, whereas entry and exit configurations exhibit weaker quantum signatures. Static fluctuations of the hopping parameters confine LGI violations to shorter time windows, while dynamic decoherence suppresses them irrespective of the hopping amplitude. Overall, our findings demonstrate that LGI-based analyses can identify stages where temporal quantum correlations are most significant, highlighting the intermediate knock-on configuration as a promising target for future studies of intrinsically quantum effects in ion-conduction phenomena.
Violations of the Leggett-Garg inequality (LGI) up to its algebraic bound under non-Hermitian dynamics are well established theoretically. Here, we demonstrate that such extreme violations are intrinsically fragile when realistic measurement processes are taken into account. We consider an open two-level system described by a time-local hybrid Liouvillian, with a continuous parameter q∈[0,1]q \in [0,1]q∈[0,1], representing detector efficiency, i.e., the fraction of quantum jump trajectories that are retained in the ensemble. This parameter interpolates between trace-preserving Lindblad dynamics (q=1q=1q=1) and non-Hermitian ``no-jump" evolution (q=0q=0q=0). While K3K_3K3​ approaches its algebraic maximum of 3 in the null-efficiency limit, even an infinitesimal increase in detector efficiency induces a rapid, highly nonlinear suppression toward the classical bound. This logarithmic sensitivity reveals that maximal LGI violations are not robust physical features but rather singular limits of idealized measurement conditions. Our results have direct experimental implications: achieving algebraic LGI violations in systems undergoing continuous time evolution requires near-perfect suppression of detected quantum jumps (i.e., effective post-selection), placing stringent constraints on detector performance. In contrast to discrete protocols based on time-non-divisible dynamics, our framework shows that extreme violations arising within continuous, divisible quantum trajectory evolution constitute a fundamentally fragile regime.