Optimal Control of Bipartite Quantum Systems

TL;DR

This paper develops optimal control strategies for bipartite quantum systems, focusing on generating and stabilizing entangled states efficiently using analytical solutions and the Pontryagin Maximum Principle.

Contribution

It introduces a reduced control system approach based on the Schmidt decomposition and provides explicit analytical solutions for controlling two-qubit and two-qutrit systems.

Findings

Explicit solutions for two-qubit systems

Control strategies for entanglement generation

Application of Pontryagin Maximum Principle

Abstract

Closed bipartite quantum systems subject to fast local unitary control are studied using quantum optimal control theory and a method of reduced control systems based on the Schmidt decomposition. Particular focus is given to the time-optimal generation of maximally entangled states and product states, as well as to the problem of stabilizing quantum states with a certain amount of entanglement. Explicit analytical solutions are given for general systems consisting of two qubits (as well as for bosonic and fermionic analogues) and also for a class of systems consisting of two coupled qutrits which is studied using the Pontryagin Maximum Principle.