Von Neumann Entropy from Mean Spin Vector

TL;DR

This paper demonstrates that for a pure entangled state of two two-level atoms, the von Neumann entropy of the partial trace can be directly measured from the mean spin vector of a single atom, simplifying entropy measurement without full state knowledge.

Contribution

It introduces a method to measure von Neumann entropy directly from the mean spin vector in two-level atomic systems, bypassing the need for complete state reconstruction.

Findings

Von Neumann entropy can be obtained from mean spin vector magnitude.

Method applicable without knowing the exact quantum state.

Applicable to other two-level quantum systems.

Abstract

We show for a general pure entangled state of two two-level atoms, the von Neumann entropy of the partial traces can be directly measured from the magnitude of the mean spin vector of a single atom of the pair. We emphasize the fact that the von Neumann entropy of the partial traces for such a system can be obtained without knowing the exact form of the quantum state of the two atoms, if we have the value of the magnitude of the mean spin vector of a single atom of the pair. Mean spin vector, used in the context of spin squeezing and spectroscopic squeezing in population spectroscopy, is experimentally measurable and provides an exact measure of von Neumann entropy of the partial traces for such a system. The idea developed in this paper can be used in the context of other quantum mechanical two level systems as the algebra of two level systems can be described by that of spin- $\frac{1}{2}$ particles.