Optimal tracking for pairs of qubit states

TL;DR

This paper develops an optimal quantum tracking strategy for transforming a single qubit into a target state based on its preparation, with applications in quantum state discrimination, purification, stabilization, and cloning.

Contribution

It introduces a universally optimal quantum tracking method for single qubits that extends existing results in state discrimination and cloning.

Findings

Proposed a tracking strategy proven to be optimal for any input and target states.

Extended existing optimality results in quantum state discrimination and cloning.

Applied the strategy to various quantum information tasks with improved performance.

Abstract

In classical control theory, tracking refers to the ability to perform measurements and feedback on a classical system in order to enforce some desired dynamics. In this paper we investigate a simple version of quantum tracking, namely, we look at how to optimally transform the state of a single qubit into a given target state, when the system can be prepared in two different ways, and the target state depends on the choice of preparation. We propose a tracking strategy that is proved to be optimal for any input and target states. Applications in the context of state discrimination, state purification, state stabilization and state-dependent quantum cloning are presented, where existing optimality results are recovered and extended.