Uncertainty, von Neumann Entropy, and Squeezing in a Bipartite State of Two-Level Atoms

TL;DR

This paper explores the complex relationship between uncertainty, von Neumann entropy, and squeezing in entangled two-level atomic systems, revealing cases where entropy and uncertainty behave counterintuitively.

Contribution

It introduces a generalized framework linking entropy, uncertainty, and squeezing in bipartite entangled states, challenging conventional assumptions about their correlations.

Findings

Entangled states can have lower entropy but higher uncertainty than subsystems.

Violations of entropic inequalities occur for certain superposition parameters.

Provides generalized relationships between entropy and squeezing parameters.

Abstract

We provide a generalized treatment of uncertainties, von Neumann entropy, and squeezing in entangled bipartite pure state of two-level atoms. We observe that when the bipartite state is entangled, though the von Neumann entropy of the composite state is less than those of the subsystems, as first recognized by Schr$\ddot{o}$dinger, but the uncertainty of the composite state is greater than those of the subsystems for certain ranges of the superposing constants of the quantum state. This is in contradiction with the prevailing idea that the greater the entropy, the greater the uncertainty. Hence, for those ranges of the superposing constants of the quantum state, although the entropic inequalities are violated, the subsystems exhibit less disorder than the system as a whole. We also present generalized relationships between the von Neumann entropies of the subsystems and the uncertainty, spin squeezing, and spectroscopic squeezing parameters - used in the context of Ramsey spectroscopy - of the composite state. This provides a generalized operational measure of von Neumann entropy of entangled subsystems of two-level atoms.