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

Asma Bashir; Hafiz Muhammad Asif Javed; Muhammad Abdul Wasay; Muhammad Shabir Mahr; Muhammad Zafar Iqbal

doi:10.1140/epjc/s10052-024-13182-x

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 815
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

Asma Bashir¹^a, Hafiz Muhammad Asif Javed¹, Muhammad Abdul Wasay³, Muhammad Shabir Mahr¹ and Muhammad Zafar Iqbal²

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

^a kbasmabashir807@gmail.com

Received: 19 May 2024
Accepted: 29 July 2024
Published online: 14 August 2024

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

© The Author(s) 2024

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