Control of population and entanglement of two qubits under the action of different types of dissipative noise

Abstract

We investigate the quantum control of two qubits interacting with a Markovian environment and evolving as an $X$ state. The control is implemented via a simple applied field, whose profile is determined by means of the piecewise time-independent quantum control method. The goal is to make either the population or the system concurrence to follow a specified tracking control trajectory. By considering the system under the influence of three kinds of noise---phase damping, amplitude damping, or a combination of both---we unveil the conditions (like energy balance) under which the quantum control is properly achieved and fidelity (monitored through the trace distance) is kept satisfactorily high, even if the qubits interact differently with the dissipative medium. We further find that the effects of phase damping, a type of noise which notoriously destroys coherence and entanglement, can be mitigated if during the control the system is also exposed to amplitude damping. Of potential interest for the usage of entanglement as resource for quantum information, our results indicate that distinct entanglement measures and coherence can be maintained relatively high (even at long times) as a consequence of the tracking quantum control process.