A simple model of quantum trajectories

Abstract

Quantum trajectory theory, developed largely in the quantum optics community to describe open quantum systems subjected to continuous monitoring, has applications in many areas of quantum physics. In this paper I present a simple model, using two-level quantum systems (q-bits), to illustrate the essential physics of quantum trajectories and how different monitoring schemes correspond to different ``unravelings'' of a mixed state master equation. I also comment briefly on the relationship of the theory to the Consistent Histories formalism and to spontaneous collapse models.

42 pages RevTeX including four figures in encapsulated postscript. Submitted to special issue of American Journal of Physics

References in corpus (5)

• Continuous quantum measurement and Itô formalism
• Controlled entanglement of two field modes in a Cavity Quantum Electrodynamics experiment
• Generalized stochastic Schroedinger equations for state vector collapse
• Quantum Computing and Nuclear Magnetic Resonance
• Recent Results in Trapped-Ion Quantum Computing

Cited by in corpus (192)

• Introduction to Quantum Noise, Measurement and Amplification
• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• Quantum control theory and applications: A survey
• A Straightforward Introduction to Continuous Quantum Measurement
• Theory of single-photon transport in a single-mode waveguide coupled to a cavity containing a two-level atom
• Measurement-Induced Entanglement Transitions in the Quantum Ising Chain: From Infinite to Zero Clicks
• Entanglement transition from variable-strength weak measurements
• Quantum collision models: open system dynamics from repeated interactions
• Self-Organized Error Correction in Random Unitary Circuits with Measurement
• Weak measurements are universal
• Continuous and Pulsed Quantum Zeno Effect
• Quantum Trajectory Approach to the Stochastic Thermodynamics of a Forced Harmonic Oscillator
• The SLH framework for modeling quantum input-output networks
• Charge and spin transport in strongly correlated one-dimensional quantum systems driven far from equilibrium
• Mechanism of decoherence-free coupling between giant atoms
• Zeno effect for quantum computation and control
• Collision model for non-Markovian quantum dynamics
• Qubit models of weak continuous measurements
• Asymptotic Improvements to Quantum Circuits via Qutrits
• Synchronization and bistability of qubit coupled to a driven dissipative oscillator
• System-environment correlations and Markovian embedding of quantum non-Markovian dynamics
• Scanning Quantum Decoherence Microscopy
• Collision models in quantum optics
• Measurement-induced steering of quantum systems
• Time Series Quantum Reservoir Computing with Weak and Projective Measurements
• Stabilization of Finite-Energy Gottesman-Kitaev-Preskill States
• A discrete invitation to quantum filtering and feedback control
• Quantum synchronization and entanglement of two qubits coupled to a driven dissipative resonator
• Rapid State-Reduction of Quantum Systems Using Feedback Control
• Probing a Gravitational Cat State
• Noisy quantum metrology enhanced by continuous nondemolition measurement
• Monitored Open Fermion Dynamics: Exploring the Interplay of Measurement, Decoherence, and Free Hamiltonian Evolution
• Collisional picture of quantum optics with giant emitters
• Symmetries and noise in quantum walk
• Quantum risk-sensitive estimation and robustness
• The Structure of Quantum Stochastic Processes with Finite Markov Order
• Hitting time for the continuous quantum walk
• Full counting statistics as probe of measurement-induced transitions in the quantum Ising chain
• Quantum synchronization
• Entropy production and asymptotic factorization via thermalization: a collisional model approach
• Large fluctuations of the first detected quantum return time
• An Efficient Quantum Jump Method for Coherent Energy Transfer Dynamics in Photosynthetic Systems under the Influence of Laser Fields
• Modelling quantum light-matter interactions in waveguide-QED with retardation and a time-delayed feedback: matrix product states versus a space-discretized waveguide model
• Conservative chaotic map as a model of quantum many-body environment
• Teleportation in a noisy environment: a quantum trajectories approach
• Engineering Superposition States and Tailored Probes for Nano-resonators Via Open-Loop Control
• Frequency Tracking and Parameter Estimation for Robust Quantum State-Estimation
• Rapid Measurement of Quantum Systems using Feedback Control
• Encoding qubits in multimode grid states
• Monitoring approach to open quantum dynamics using scattering theory
• Feedback Control Using Only Quantum Back-Action
• Comparing Conditions for Macrorealism: Leggett-Garg Inequalities vs No-Signaling in Time
• Continuous measurement with traveling wave probes
• Feedback Control of Non-linear Quantum Systems: a Rule of Thumb
• Precursors of non-Markovianity
• Diagnosing non-Hermitian Many-Body Localization and Quantum Chaos via Singular Value Decomposition
• Equivalent definitions of the quantum nonadiabatic entropy production
• The information about the state of a qubit gained by a weakly coupled detector
• Weak and strong measurement of a qubit using a switching-based detector
• Quantum Feedback Control: How to use Verification Theorems and Viscosity Solutions to Find Optimal Protocols
• Objective trajectories in hybrid classical-quantum dynamics
• Quantum trajectories for a system interacting with environment in a single photon state: counting and diffusive processes
• Gaussian Quantum Trajectories for the Variational Simulation of Open Quantum-Optical Systems
• Quantum trajectory analysis of single microwave photon detection by nanocalorimetry
• Simulating noisy quantum protocols with quantum trajectories
• Rapid purification of quantum systems by measuring in a feedback-controlled unbiased basis
• Stochastic Bloch-Redfield theory: quantum jumps in a solid-state environment
• A pedagogical introduction to continuously monitored quantum systems and measurement-based feedback
• Analysis of the quantum Zeno effect for quantum control and computation
• Quantum and classical correlations in open quantum-spin lattices via truncated-cumulant trajectories
• Adaptive variational simulation for open quantum systems
• Quantum trajectories for time-dependent adiabatic master equations
• Estimation of quantum states by weak and projective measurements
• The Quantum Theory of MIMO Markovian Feedback with Diffusive Measurements
• Test of weak measurement on a two- or three-qubit computer
• Quantum Correlation Sharing: A Review On Recent Progress From Nonlocality To Other Non-Classical Correlations
• Density and current statistics in boundary-driven monitored fermionic chains
• Quantum resetting in continuous measurement induced dynamics of a qubit
• Adiabatic evolution under quantum control
• Measuring Fluorescence to Track a Quantum Emitter's State: A Theory Review
• Replacing Quantum Feedback with Open-Loop Control and Quantum Filtering
• Quantum enhancement of a single quantum battery by repeated interactions with large spins
• Quantum master equations for entangled qubit environments
• Collision model for non-Markovian quantum trajectories
• Quantum trajectories for a system interacting with environment in N-photon state
• Noise gates for decoherent quantum circuits
• Chaos in Continuously Monitored Quantum Systems: An Optimal Path Approach
• Quantum communication via a continuously monitored dual spin chain
• Atomic Quantum Technologies for Quantum Matter and Fundamental Physics Applications
• Dissipative quantum chaos: transition from wave packet collapse to explosion
• Dissipative decoherence in the Grover algorithm
• Feedback-assisted quantum search by continuous-time quantum walks
• Steady-state generation of Wigner negative states in 1D resonance fluorescence
• Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain
• Quantum Trajectory Theory and Simulations of Nonlinear Spectra and Multi-Photon Effects in Waveguide-QED Systems with a Time-Delayed Coherent Feedback
• Engineering two-qubit mixed states with weak measurements
• Scrambling and operator entanglement in local non-Hermitian quantum systems
• Dissipative state transfer and Maxwell's demon in single quantum trajectories: Excitation transfer between two noninteracting qubits via unbalanced dissipation rates
• Strategies to simulate dephasing-assisted quantum transport on digital quantum computers
• Quantum state engineering by steering in the presence of errors
• Collision model approach to steering of an open driven qubit
• Local disclosure of quantum memory in non-Markovian dynamics
• Quantum Zeno Effect of General Quantum Operations
• Quantum chaos algorithms and dissipative decoherence with quantum trajectories
• Entanglement-Preserving Limit Cycles from Sequential Quantum Measurements and Feedback
• From a posteriori to a priori solutions for a two-level system interacting with a single-photon wavepacket
• Dancing the Quantum Waltz: Compiling Three-Qubit Gates on Four Level Architectures
• Memory Effects in Quantum Processes
• Physics of PT-Symmetric Quantum Systems at Finite Temperature
• Quantum homogenization in non-Markovian collisional model
• Method for quantum-jump continuous-time quantum error correction
• A Simple game simulating quantum measurements of qubits
• Observables in non-Hermitian systems: A methodological comparison
• Maximum information gain in weak or continuous measurements of qudits: complementarity is not enough
• Solving quantum trajectories for systems with linear Heisenberg-picture dynamics and Gaussian measurement noise
• Non-Hermitian and Zeno limit of quantum systems under rapid measurements
• Weakly measured while loops: peeking at quantum states
• Continuous measurement of a qudit using dispersively coupled radiation
• Decomposing generalized measurements into continuous stochastic processes
• Quantum trajectories in spin-exchange collisions reveal the nature of spin-noise correlations in multi-species alkali vapors
• Robust and efficient generator of almost maximal multipartite entanglement
• Sequential generalized measurements: Asymptotics, typicality and emergent projective measurements
• Catalysis always degrades external quantum correlations
• Optimal Zeno Dragging for Quantum Control: A Shortcut to Zeno with Action-based Scheduling Optimization
• Entangled-State Cycles of Atomic Collective-Spin States
• How to design quantum-jump trajectories via distinct master equation representations
• Fluctuations and stability of a fast driven Otto cycle
• Quantum trajectories for environment in superposition of coherent states
• Microscopic biasing of discrete-time quantum trajectories
• Implementing quantum stochastic differential equations on a quantum computer
• Quantum non-Markovian collision models from colored-noise baths
• Entanglement of a pair of quantum emitters via continuous fluorescence measurements: a tutorial
• Consistent histories for tunneling molecules subject to collisional decoherence
• Quantum dynamics under simultaneous and continuous measurement of noncommutative observables
• Emergence of Constructor-based Irreversibility in Quantum Systems: Theory and Experiment
• Quantum state tomography of undetected photons
• Dynamical localization, measurements and quantum computing
• Theory of Metastability in Discrete-Time Open Quantum Dynamics
• How to perform the coherent measurement of a curved phase space by continuous isotropic measurement. I. Spin and the Kraus-operator geometry of $\mathrm{SL}(2,\mathbb{C})$
• Quantum feedback control in quantum photosynthesis
• Quantization of the mean decay time for non-Hermitian quantum systems
• Quantum Back-action Limits in Dispersively Measured Bose-Einstein Condensates
• Synchronization of a superconducting qubit to an optical field mediated by a mechanical resonator
• Snapshotting Quantum Dynamics at Multiple Time Points
• The Harmonic Quantum Szilárd Engine
• Breakdown of Measurement-Induced Phase Transitions Under Information Loss
• Measurement-induced entanglement transition in chaotic quantum Ising chain
• Digital homodyne and heterodyne detection for stationary bosonic modes
• Exploring the extent of validity of quantum work fluctuation theorems in the presence of weak measurements
• Work, heat and entropy production along quantum trajectories
• Rapid-purification protocols for optical homodyning
• Locality, Correlations, Information, and non-Hermitian Quantum Systems
• Continuous decomposition of quantum measurements via qubit probe feedback
• Hamiltonian Learning using Machine Learning Models Trained with Continuous Measurements
• Weak measurement-based state estimation of Gaussian states of one-variable quantum systems
• Weak stochastic ratchets and dynamic localization in measurement-induced quantum trajectories
• Simultaneous Measurements of Noncommuting Observables. Positive Transformations and Instrumental Lie Groups
• Collisional-model quantum trajectories for entangled qubit environments
• Continuous monitoring can improve indistinguishability of a single-photon source
• Qubit POVMs by destructive weak measurements
• Quantum Field Measurements in the Fewster-Verch Framework
• Making Quantum Collision Models Exact
• Optimal measurement-based feedback control for a single qubit: a candidate protocol
• Quantum synchronization and entanglement of dissipative qubits coupled to a resonator
• Hitting statistics from quantum jumps
• Algebraic and algorithmic frameworks for optimized quantum measurements
• Continuous decomposition of quantum measurements via Hamiltonian feedback
• Rapid readout of a register of qubits using open loop quantum control
• Engineering Quantum States, Nonlinear Measurements, and Anomalous Diffusion by Imaging
• Work fluctuations due to partial thermalizations in two-level systems
• Telling different unravelings apart via nonlinear quantum-trajectory averages
• Strong Markov dissipation in driven-dissipative quantum systems
• Photon counting probabilities of the output field for a single-photon input
• Statistical time-domain characterization of non-periodic optical clocks
• Nonequilibrium steady states in multi-bath quantum collision models
• Decomposing qubit positive-operator valued measurements into continuous destructive weak measurements
• Efficient progressive readout of a register of (qu)bits
• Quantum optomechanical system in a Mach-Zehnder interferometer
• Gaussian approximation and single-spin measurement in OSCAR MRFM with spin noise
• Stochastic approach to evolution of a quantum system interacting with a wave packet in squeezed number state
• Kicked fluxonium with quantum strange attractor
• Continuous fuzzy measurement on two-level systems revisited
• Derive the Born's rule from environment-induced stochastic dynamics of wave-functions in an open system
• A posterior quantum dynamics for a continuous diffusion observation of a coherent channel
• Wavefunction collapse through backaction of counting weakly interacting photons
• Conditions for the Quantum to Classical Transition: Trajectories vs. Phase Space Distributions
• Unconventional mechanism of virtual-state population through dissipation
• Computational Complexity and Simulability of Non-Hermitian Quantum Dynamics
• CDJ-Pontryagin Optimal Control for General Continuously Monitored Quantum Systems
• Emergent Quantum Jumps in a Nano-Electro-Mechanical System
• Some Entanglement Survives Most Measurements
• Quantum thermodynamics under continuous monitoring: a general framework