Variance-based uncertainty relations and entanglement amplification for particles constrained on a torus

Abstract

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 $$\mathcal {\vec {B}}$$ B → . We explore the system’s parameter space and show that these new URs have field-tunable uncertainty bounds. Our analysis reveals that $$\mathcal {\vec {A}}$$ A → (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 ($$\mathcal {POV}$$ POV ). Additionally, we give the critical range of $$\mathcal {\vec {A}}$$ A → and $$\mathcal {\vec {B}}$$ B → where the system acts as an entanglement amplifier; this amplification is also discussed under various geometric parameters. The possibility of reducing the $$\mathcal {POV}$$ POV 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 $$\mathcal {\vec {B}}$$ B → by saturating the angular momentum uncertainty relation and identify the critical coherence value $${\mathcal {B}}_c$$ B c such that when $${\mathcal {B}}\ne {\mathcal {B}}_c$$ B ≠ B c , the state decoheres.