Some features of the state-space trajectories followed by robust entangled four-qubit states during decoherence

TL;DR

This paper investigates the geometric features of state-space trajectories of four-qubit entangled states under decoherence, revealing how initial robustness influences their evolution towards mixed states.

Contribution

It introduces a geometric analysis of decoherence trajectories for four-qubit states, linking initial robustness to the path in state space.

Findings

Trajectories are characterized by distances to reference states.

Initial robust states follow distinct geometric paths.

The study connects initial entanglement robustness with decoherence dynamics.

Abstract

In a recent work (Borras et al., Phys. Rev. A {\bf 79}, 022108 (2009)), we have determined, for various decoherence channels, four-qubit initial states exhibiting the most robust possible entanglement. Here we explore some geometrical features of the trajectories in state space generated by the decoherence process, connecting the initially robust pure state with the completely decohered mixed state obtained at the end of the evolution. We characterize these trajectories by recourse to the distance between the concomitant time dependent mixed state and different reference states.