Control landscape of measurement-assisted transition probability for a three-level quantum system with dynamical symmetry

Abstract

Quantum systems with dynamical symmetries have conserved quantities which are preserved under coherent controls. Therefore such systems can not be completely controlled by means of only coherent control. In particular, for such systems maximal transition probability between some pair of states over all coherent controls can be less than one. However, incoherent control can break this dynamical symmetry and increase the maximal attainable transition probability. Simplest example of such situation occurs in a three-level quantum system with dynamical symmetry, for which maximal probability of transition between the ground and the intermediate state by only coherent control is $1/2$, and by coherent control assisted by incoherent control implemented by non-selective measurement of the ground state is about $0.687$, as was previously analytically computed. In this work we study and completely characterize all critical points of the kinematic quantum control landscape for this measurement-assisted transition probability, which is considered as a function of the kinematic control parameters (Euler angles). This used in this work measurement-driven control is different both from quantum feedback and Zeno-type control. We show that all critical points are global maxima, global minima, saddle points and second order traps. For comparison, we study the transition probability between the ground and highest excited state, as well as the case when both these transition probabilities are assisted by incoherent control implemented by measurement of the intermediate state.

References in corpus (18)

• Quantum control by von Neumann measurements
• Measurement Based Feedback Quantum Control With Deep Reinforcement Learning for Double-well Non-linear Potential
• Control Landscapes for Observable Preparation with Open Quantum Systems
• Hamilton-Jacobi-Bellman equations for Quantum Filtering and Control
• Incoherent qubit control using the quantum Zeno effect
• Measurement-assisted Landau-Zener transitions
• Dynamical symmetries of periodically-driven quantum systems and their spectroscopic signatures
• Control of quantum dynamics by optimized measurements
• Feedback Control of Non-linear Quantum Systems: a Rule of Thumb
• Optimized Steering: Quantum State Engineering and Exceptional Points
• Unified analysis of terminal-time control in classical and quantum systems
• General unifying features of controlled quantum phenomena
• Measurement-based quantum thermal machines with feedback control
• Active-feedback quantum control of an integrated low-frequency mechanical resonator
• Feedback Policies for Measurement-based Quantum State Manipulation
• Quantum feedback control in quantum photosynthesis
• Measurement-Based Control for Minimizing Energy Functions in Quantum Systems
• Decoherence-assisted quantum driving

Cited by in corpus (4)

• Quantum control landscape for generation of $H$ and $T$ gates in an open qubit with both coherent and environmental drive
• Phenomenon of a stronger trapping behaviour in $\Lambda$-type quantum systems with symmetry
• Control landscapes for high-fidelity generation of C-NOT and C-PHASE gates with coherent and environmental driving
• Optimization of Time-Dependent Decoherence Rates and Coherent Control for a Qutrit System