Leggett--Garg Tests of Collective Excitation--Inhibition Dynamics in Neuronal Circuits
Abstract
Recent efforts to identify quantum-like signatures in brain and cognition have explored Bell-type tests, temporal inequalities, and Schrödinger-inspired models. We propose a Leggett--Garg (LG) test of collective neuronal excitation--inhibition (E--I) dynamics. Two reference configurations, ketE and ketI, span an effective two-state space governed by HS=heffΩσx/2. Spatial separation of the E and I complexes need not preclude coherent superposition: when they constitute distinct subsystems, the corresponding collective alternatives can form an entangled state. The proposal tests temporal correlations, not Bell nonlocality. Complementary feedforward detectors couple selectively to E or I, with ideal negative results enabling non-invasive inference of the opposite configuration. We give a four-output-cell realization of the required projectors and detector interactions. Ideal sequential measurements yield K3(τ)=2cos(Ωτ)−cos(2Ωτ), reaching 3/2. We also derive the four-time result K4max=2√2 and explain its structural CHSH correspondence through Choi--Jamiołkowski duality. Detector efficiency, false positives, imperfect null results, timing uncertainty, and measurement disturbance are incorporated into a realistic extension. We conclude by identifying the experimental challenges of preparing, controlling, and selectively measuring collective E--I states in neuronal circuits.
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BibTeX
@misc{ghose2026leggettgarg,
title = {{Leggett--Garg Tests of Collective Excitation--Inhibition Dynamics in Neuronal Circuits}},
author = {Partha Ghose},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.12126},
eprint = {2605.12126},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.12126},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Leggett--Garg Tests of Collective Excitation--Inhibition Dynamics in Neuronal Circuits
AU - Partha Ghose
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2605.12126
UR - https://arxiv.org/abs/2605.12126
AB - Recent efforts to identify quantum-like signatures in brain and cognition have explored Bell-type tests, temporal inequalities, and Schrödinger-inspired models. We propose a Leggett--Garg (LG) test of collective neuronal excitation--inhibition (E--I) dynamics. Two reference configurations, ketE and ketI, span an effective two-state space governed by H_S=heffΩσ_x/2. Spatial separation of the E and I complexes need not preclude coherent superposition: when they constitute distinct subsystems, the corresponding collective alternatives can form an entangled state. The proposal tests temporal correlations, not Bell nonlocality. Complementary feedforward detectors couple selectively to E or I, with ideal negative results enabling non-invasive inference of the opposite configuration. We give a four-output-cell realization of the required projectors and detector interactions. Ideal sequential measurements yield K_3(τ)=2cos(Ωτ)−cos(2Ωτ), reaching 3/2. We also derive the four-time result K_4^max=2√2 and explain its structural CHSH correspondence through Choi--Jamiołkowski duality. Detector efficiency, false positives, imperfect null results, timing uncertainty, and measurement disturbance are incorporated into a realistic extension. We conclude by identifying the experimental challenges of preparing, controlling, and selectively measuring collective E--I states in neuronal circuits.
ER -