# Schr\"odinger cat and Werner state disentanglement simulated by trapped ion systems

## TL;DR

This paper models and analyzes the disentanglement of Schr"odinger cat and Werner states in trapped ion systems under noise, revealing a sudden transition in decay regimes driven by classical collective noise.

## Contribution

It provides an analytical framework for quantum correlation dynamics in trapped ion states, including a novel observation of a sudden transition between classical and quantum decay regimes.

## Key findings

- Schr"odinger cat states' entanglement vanishes asymptotically under vacuum noise.
- Werner states' entanglement shows robustness and can recover during noiseless-like evolution.
- A first report of a sudden transition between classical and quantum decay regimes driven by classical noise.

## Abstract

Disentanglement and loss of quantum correlations due to one global collective noise effect are described for two-qubit Schr\"odinger cat and Werner states of a four level trapped ion quantum system. Once the Jaynes-Cummings ionic interactions are mapped onto a Dirac spinor structure, the elementary tools for computing quantum correlations of two-qubit ionic states are provided. With two-qubit quantum numbers related to the total angular momentum and to its projection onto the direction of an external magnetic field (which lifts the degeneracy of the ion's internal levels), a complete analytical profile of entanglement for the Schr\"odinger cat and Werner states is obtained. Under vacuum noise (during spontaneous emission), the two-qubit entanglement in the Schr\"odinger cat states is shown to vanish asymptotically. Otherwise, the robustness of Werner states is concomitantly identified, with the entanglement content recovered by their noiseless-like evolution. Most importantly, our results point to a firstly reported sudden transition between classical and quantum decay regimes driven by a classical collective noise on the Schr\"odinger cat states, which has been quantified by the geometric discord.