# Disentanglement in a quantum critical environment

## TL;DR

This paper investigates how entanglement between two qubits or qutrits decays over time when coupled to a quantum critical environment, revealing exponential decay near the critical point.

## Contribution

It provides explicit relationships between entanglement measures and decoherence factors in a quantum critical environment, highlighting the decay behavior near phase transitions.

## Key findings

- Entanglement decays exponentially with the fourth power of time near the critical point.
- Explicit formulas relate concurrence and negativity to decoherence factors.
- Decay behavior depends on initial states, such as maximally entangled or Werner states.

## Abstract

We study the dynamical process of disentanglement of two qubits and two qutrits coupled to an Ising spin chain in a transverse field, which exhibits a quantum phase transition. We use the concurrence and negativity to quantify entanglement of two qubits and two qutrits, respectively. Explicit connections between the concurrence (negativity) and the decoherence factors are given for two initial states, the pure maximally entangled state and the mixed Werner state. We find that the concurrence and negativity decay exponentially with fourth power of time in the vicinity of critical point of the environmental system.