Time evolution of Two-qubit Entanglement

TL;DR

This paper models the time evolution of entanglement in two-qubit systems using a 10-dimensional differential equation, providing analytic solutions for physical examples like Josephson junction qubits, aiding quantum information processing.

Contribution

It introduces a novel 10-dimensional differential equation framework for entanglement dynamics, linking Hamiltonian parameters to entanglement behavior and offering analytic solutions for specific quantum systems.

Findings

Entanglement evolution is governed by a 10D complex differential equation.

Hamiltonian coefficients determine whether entanglement is periodic.

Analytic solutions are derived for Josephson junction qubits.

Abstract

We show that the entanglement dynamics for a closed two-qubit system is part of a 10-dimensional complex linear differential equation defined on a supersphere, and the coefficients therein are completely determined by the Hamiltonian. We apply the result to investigate two physical examples of Josephson junction qubits and exchange Hamiltonians, deriving analytic solutions for the time evolution of entanglement. The Hamiltonian coefficients determines whether the entanglement is periodic. These results allow of investigating how to generate and manipulate entanglements efficiently, which are required by both quantum computation and quantum communication.