Optimized Steering: Quantum State Engineering and Exceptional Points

TL;DR

This paper explores quantum state steering using weak measurements and Hamiltonian control, revealing that optimal steering dynamics are governed by exceptional points, with phase transitions between relaxational and oscillatory behaviors.

Contribution

It demonstrates that any quantum state can be targeted through optimized weak measurement protocols and links the dynamics to Liouvillian exceptional points, highlighting a phase transition in steering behavior.

Findings

Optimal steering can target any quantum state.

Liouvillian exceptional points underlie the dynamics.

A phase transition occurs between relaxational and oscillatory regimes.

Abstract

The state of a quantum system may be steered towards a predesignated target state, employing a sequence of weak $\textit{blind}$ measurements (where the detector's readouts are traced out). Here we analyze the steering of a two-level system using the interplay of a system Hamiltonian and weak measurements, and show that $\textit{any}$ pure or mixed state can be targeted. We show that the optimization of such a steering protocol is underlain by the presence of Liouvillian exceptional points. More specifically, for high purity target states, optimal steering implies purely relaxational dynamics marked by a second-order exceptional point, while for low purity target states, it implies an oscillatory approach to the target state. The dynamical phase transition between these two regimes is characterized by a third-order exceptional point.