Asymptotic Entanglement Dynamics and Geometry of Quantum States

TL;DR

This paper classifies the long-term entanglement behaviors of quantum systems based on the geometry of their asymptotic states, providing explicit examples and analyzing probabilities for different initial states.

Contribution

It offers a refined classification of asymptotic entanglement dynamics using geometric insights and supplies explicit examples for each class, enhancing previous theoretical frameworks.

Findings

Explicit examples for all classes of asymptotic entanglement behavior.

Probabilities of different behaviors for random initial states.

Geometric classification improves understanding of entanglement dynamics.

Abstract

A given dynamics for a composite quantum system can exhibit several distinct properties for the asymptotic entanglement behavior, like entanglement sudden death, asymptotic death of entanglement, sudden birth of entanglement, etc. A classification of the possible situations was given in [M. O. Terra Cunha, {\emph{New J. Phys}} {\bf{9}}, 237 (2007)] but for some classes there were no known examples. In this work we give a better classification for the possibile relaxing dynamics at the light of the geometry of their set of asymptotic states and give explicit examples for all the classes. Although the classification is completely general, in the search of examples it is sufficient to use two qubits with dynamics given by differential equations in Lindblad form (some of them non-autonomous). We also investigate, in each case, the probabilities to find each possible behavior for random initial states.