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Variance-based uncertainty relations and entanglement amplification for particles constrained on a torus
- Source :
- European Physical Journal C: Particles and Fields, Vol 84, Iss 8, Pp 1-16 (2024)
- Publication Year :
- 2024
- Publisher :
- SpringerOpen, 2024.
-
Abstract
- 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.
Details
- Language :
- English
- ISSN :
- 14346052
- Volume :
- 84
- Issue :
- 8
- Database :
- Directory of Open Access Journals
- Journal :
- European Physical Journal C: Particles and Fields
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.9463293490944dac8335c130c78f7d9f
- Document Type :
- article
- Full Text :
- https://doi.org/10.1140/epjc/s10052-024-13182-x