Constrained dynamics of maximally entangled bipartite system

TL;DR

This paper investigates the constrained quantum dynamics of maximally entangled bipartite systems on a circle, revealing how external fields influence entanglement, dispersion, and energy shifts, with implications for controlling quantum states.

Contribution

It introduces a framework for tuning external fields to control entanglement and dispersion in bipartite systems constrained on a circle, including bounds for entanglement loss.

Findings

Maximal entanglement reduces measurement dispersion

External field bounds determine entanglement preservation

Energy shifts occur due to Hermiticity constraints

Abstract

The classical and quantum dynamics of two particles constrained on $S^1$ is discussed via Dirac's approach. We show that when state is maximally entangled between two subsystems, the product of dispersion in the measurement reduces. We also quantify the upper bound on the external field $\vec{B}$ such that $\vec{B}\geq\vec{B}_{upper}$ implies no reduction in the product of dispersion pertaining to one subsystem. Further, we report on the cut-off value of the external field $\vec{B}_{cutoff}$, above which the bipartite entanglement is lost and there exists a direct relationship between uncertainty of the composite system and the external field. We note that, in this framework it is possible to tune the external field for entanglement/unentanglement of a bipartite system. Finally, we show that the additional terms arising in the quantum Hamiltonian, due to the requirement of Hermiticity of operators, produce a shift in the energy of the system.