https://doi.org/10.1140/epjc/s10052-024-13182-x
Regular Article – Theoretical Physics
Variance-based uncertainty relations and entanglement amplification for particles constrained on a torus
1
Department of Physics, University of Agriculture, 38040, Faisalabad, Pakistan
2
Department of Mathematics and Statistics, University of Agriculture, 38040, Faisalabad, Pakistan
3
School of Theoretical Physics, Hunan University, 410082, Changsha, China
Received:
19
May
2024
Accepted:
29
July
2024
Published online:
14
August
2024
We formulate the variance-based uncertainty relations (URs) via the Robertson’s inequality, for a 2-particle entangled system constrained on a torus and subject to a stationary magnetic field 
. We explore the system’s parameter space and show that these new URs have field-tunable uncertainty bounds. Our analysis reveals that 
(vector potential) induces a phase shift in the state, due to the Aharonov–Bohm effect, leading to a perturbed system dynamics which results in asymmetric product of variance (
). Additionally, we give the critical range of and where the system acts as an entanglement amplifier; this amplification is also discussed under various geometric parameters. The possibility of reducing the of the conjugate pair [q, p] below the known benchmark value by the Generalized Uncertainty Relation (GUR) is also demonstrated. Finally, we check the susceptibility of state coherence to by saturating the angular momentum uncertainty relation and identify the critical coherence value 
such that when 
, the state decoheres.
© The Author(s) 2024
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