Optimized Steering: Quantum State Engineering and Exceptional Points

Abstract

The state of a quantum system may be steered towards a predesignated target state, employing a sequence of weak $\text{blind}$ 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 $\text{any}$ 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.

arXiv comment6 pages + 4 pages supplementary information, 2 figures

References in corpus (50)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• Quantum information with Rydberg atoms
• Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Non-Hermitian Physics
• The physics of exceptional points
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• A Rydberg Quantum Simulator
• Preparation of Entangled States by Quantum Markov Processes
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Topology by Dissipation in Atomic Quantum Wires
• Metrology with $\mathcal{P}\mathcal{T}$-symmetric cavities: Enhanced sensitivity near the $\mathcal{P}\mathcal{T}$-phase transition
• Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
• Dissipative production of a maximally entangled steady state
• High-Fidelity Entanglement and Detection of Alkaline-Earth Rydberg Atoms
• Non-Hermitian Quantum Sensing: Fundamental Limits and Non-Reciprocal Approaches
• Stabilizing entanglement autonomously between two superconducting qubits
• Quantum Noise Theory of Exceptional Point Sensors
• Inverse design of third-order Dirac exceptional points in photonic crystals
• Petermann-factor limited sensing near an exceptional point
• Cavity-assisted quantum bath engineering
• Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories
• Quantum jumps in the non-Hermitian dynamics of a superconducting qubit
• Analysis of quantum semigroups with GKS--Lindblad generators II. General
• Universal stabilization of a parametrically coupled qubit
• Realization of a $\Lambda$ system with metastable states of a capacitively-shunted fluxonium
• Quantum control by von Neumann measurements
• Stabilizing a Bell state of two superconducting qubits by dissipation engineering
• Nanowire Superinductance Fluxonium Qubit
• Measurement-induced steering of quantum systems
• Pfaffian State Generation by Strong 3-Body Dissipation
• Comparing and combining measurement-based and driven-dissipative entanglement stabilization
• Robustness of exceptional-point-based sensors against parametric noise: The role of Hamiltonian and Liouvillian degeneracies
• Liouvillian exceptional points of any order in dissipative linear bosonic systems: Coherence functions and switching between $\mathcal{P}\mathcal{T}$ and anti-$\mathcal{P}\mathcal{T}$ symmetries
• Signatures of Liouvillian exceptional points in a quantum thermal machine
• Engineering arbitrary pure and mixed quantum states
• Exceptional points of the Lindblad operator of a two-level system
• Control-free control: manipulating a quantum system using only a limited set of measurements
• Optimized heat transfer at exceptional points in quantum circuits
• Hybrid quantum computation gate with trapped ion system
• Measurement driven quantum evolution
• Feedback Control Using Only Quantum Back-Action
• Nonreciprocal Signal Routing in an Active Quantum Network
• Hamiltonian Control of Quantum Dynamical Semigroups: Stabilization and Convergence Speed
• Quantum optimal control of the dissipative production of a maximally entangled state
• Direct reconstruction of the quantum master equation dynamics of a trapped ion qubit
• Engineering two-qubit mixed states with weak measurements
• Universal stabilization of single-qubit states using a tunable coupler
• Thermal Motors with Enhanced Performance due to Engineered Exceptional Points

Cited by in corpus (18)

• Engineered Dissipation for Quantum Information Science
• Decoherence Induced Exceptional Points in a Dissipative Superconducting Qubit
• Quantum discord and steering in top quarks at the LHC
• Observation of quantum strong Mpemba effect
• Accelerating relaxation through Liouvillian exceptional point
• State Preparation on Quantum Computers via Quantum Steering
• Chiral Bell-state transfer via dissipative Liouvillian dynamics
• Arnoldi-Lindblad time evolution: Faster-than-the-clock algorithm for the spectrum of time-independent and Floquet open quantum systems
• Engineering unsteerable quantum states with active feedback
• Localization, fractality, and ergodicity in a monitored qubit
• Quantum state engineering by steering in the presence of errors
• Topological transitions in quantum jump dynamics: Hidden exceptional points
• Optimal Zeno Dragging for Quantum Control: A Shortcut to Zeno with Action-based Scheduling Optimization
• Liouvillian exceptional points of an open driven two-level system
• Engineering nonequilibrium steady states through Floquet Liouvillians
• Control landscape of measurement-assisted transition probability for a three-level quantum system with dynamical symmetry
• Generation of Volume-Law Entanglement by Local-Measurement-Only Quantum Dynamics
• Non-Hermiticity induced thermal entanglement phase transition