Quantum Zeno dynamics: mathematical and physical aspects

Abstract

If frequent measurements ascertain whether a quantum system is still in its initial state, transitions to other states are hindered and the quantum Zeno effect takes place. However, in its broader formulation, the quantum Zeno effect does not necessarily freeze everything. On the contrary, for frequent projections onto a multidimensional subspace, the system can evolve away from its initial state, although it remains in the subspace defined by the measurement. The continuing time evolution within the projected "quantum Zeno subspace" is called "quantum Zeno dynamics:" for instance, if the measurements ascertain whether a quantum particle is in a given spatial region, the evolution is unitary and the generator of the Zeno dynamics is the Hamiltonian with hard-wall (Dirichlet) boundary conditions. We discuss the physical and mathematical aspects of this evolution, highlighting the open mathematical problems. We then analyze some alternative strategies to obtain a Zeno dynamics and show that they are physically equivalent.

52 pages, 10 figures

References in corpus (70)

• Dynamical suppression of decoherence in two-state quantum systems
• Noiseless Quantum Codes
• Quantum Computers and Dissipation
• Preserving coherence in quantum computation by pairing quantum bits
• Quantum Zeno subspaces
• Quantum Computing Using Dissipation to Remain in a Decoherence-Free Subspace
• Protecting entanglement via the quantum Zeno effect
• Observation of the Quantum Zeno and Anti-Zeno effects in an unstable system
• Unification of Dynamical Decoupling and the Quantum Zeno Effect
• From the quantum Zeno to the inverse quantum Zeno effect
• Decoherence-Free Subspaces and Subsystems
• Quantum Zeno effect by general measurements
• Control of decoherence: analysis and comparison of three different strategies
• Temporal behavior of quantum mechanical systems
• Quantum Logic Operations Using Single Photons and the Zeno Effect
• Quantum Computing Using Single Photons and the Zeno Effect
• Continuous and Pulsed Quantum Zeno Effect
• Quantum Zeno Dynamics
• Non-exponential decay via tunneling in tight-binding lattices and the optical Zeno effect
• Quantum Bi-Hamiltonian Systems
• Projection Postulate and Atomic Quantum Zeno Effect
• Universal dynamical decoherence control of noisy single-and multi-qubit systems
• Purification through Zeno-like Measurements
• Temporal behavior and quantum Zeno time of an excited state of the hydrogen atom
• Environmentally induced Quantum Dynamical Phase Transition in the spin swapping operation
• Quantum anti-Zeno effect
• Zeno dynamics yields ordinary constraints
• Zeno and anti-Zeno effects for quantum Brownian motion
• Preparation and Entanglement Purification of Qubits through Zeno-like Measurements
• The Quantum Zeno Effect - Evolution of an Atom Impeded by Measurement
• Strongly Coupled Quantum and Classical Systems and Zeno's Effect
• Understanding the quantum Zeno effect
• Wigner's Problem and Alternative Commutation Relations for Quantum Mechanics
• Spontaneous emission and lifetime modification caused by an intense electromagnetic field
• A relaxationless demonstration of the Quantum Zeno Paradox on an individual atom
• Deviations from exponential law and Van Hove's "λ^2 t" limit
• Berry phase from a quantum Zeno effect
• NMR analogues of the quantum Zeno effect
• Long-range entanglement generation via frequent measurements
• Product formula related to quantum Zeno dynamics
• Decoherence and the Quantum Zeno Effect
• What does an observed quantum system reveal to its observer ?
• Absorption-free optical control of spin systems:the quantum Zeno effect in optical pumping
• Unstable Systems in Relativistic Quantum Field Theory
• Measurement-induced quantum diffusion
• Quantum Zeno and anti-Zeno effects in the Friedrichs model
• Quantum Zeno effect in a probed downconversion process
• The role of initial state reconstruction in short and long time deviations from exponential decay
• General equation for Zeno-like effects in spontaneous exponential decay
• Distillation of Entanglement between Distant Systems by Repeated Measurements on Entanglement Mediator
• Time Evolution of Unstable Particle Decay Seen with Finite Resolution
• Quantum Zeno tomography
• Evolution of an Atom Impeded by Measurement: The Quantum Zeno Effect
• Quantum Zeno Effect in Trapped Ions
• Theory of multiwave mixing and decoherence control in qubit array system
• Distilling angular momentum nonclassical states in trapped ions
• Consistent histories, the quantum Zeno effect, and time of arrival
• Qubit state guidance without feedback
• A Simple Scheme to Entangle Distant Qubits from a Mixed State via an Entanglement Mediator
• On the Absence of the Zeno Effect in Relativistic Quantum Field Theory
• Zeno product formula revisited
• Suppression of Zeno effect for distant detectors
• Zeno Dynamics in Quantum Statistical Mechanics
• Correcting low-frequency noise with continuous measurement
• Influence of dissipation on the extraction of quantum states via repeated measurements
• Zeno dynamics and constraints
• Stability and instability in parametric resonance and quantum Zeno effect
• Estimation of the Repeatedly-Projected Reduced Density Matrix under Decoherence
• Zeno Dynamics of von Neumann Algebras
• Three different manifestations of the quantum Zeno effect

Cited by in corpus (255)

• Quantum metrology with nonclassical states of atomic ensembles
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Simulating Lattice Gauge Theories within Quantum Technologies
• Engineered Dissipation for Quantum Information Science
• Constrained dynamics via the Zeno effect in quantum simulation: Implementing non-Abelian lattice gauge theories with cold atoms
• Experimental realization of quantum zeno dynamics
• The ultimate precision limits for noisy frequency estimation
• Confined quantum Zeno dynamics of a watched atomic arrow
• Mechanism of decoherence-free coupling between giant atoms
• Deterministic generation of multiparticle entanglement by quantum Zeno dynamics
• Zeno effect for quantum computation and control
• Quantum Zeno Effect Explains Magnetic-Sensitive Radical-Ion-Pair Reactions
• Dissipation Induced Nonstationarity in a Quantum Gas
• Measurement-induced dynamics of many-body systems at quantum criticality
• Quantum Dynamics in Krylov Space: Methods and Applications
• Algebraic Theory of Quantum Synchronization and Limit Cycles under Dissipation
• Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems
• Quantum Zeno dynamics of a field in a cavity
• Coherent and dissipative dynamics at quantum phase transitions
• Detection of a quantum particle on a lattice under repeated projective measurements
• Phase space tweezers for tailoring cavity fields by quantum Zeno dynamics
• Long-time behavior of many-particle quantum decay
• Discrete Abelian Gauge Theories for Quantum Simulations of QED
• Exact dynamics of non-additive environments in non-Markovian open quantum systems
• Quantum Zeno dynamics and quantum Zeno subspaces
• Influence of measurements on the statistics of work performed on a quantum system
• Multipartite Entangled Spatial Modes of Ultracold Atoms Generated and Controlled by Quantum Measurement
• Fundamental limits to frequency estimation: A comprehensive microscopic perspective
• Dissipative preparation of steady Greenberger-Horne-Zeilinger states for Rydberg atoms with quantum Zeno dynamics
• Multimode photon blockade
• Giant atoms with time-dependent couplings
• Long-time memory in non-Markovian evolutions
• Macroscopic Zeno effect and stationary flows in nonlinear waveguides with localized dissipation
• Universality in driven open quantum matter
• Experimental investigation of quantum decay at short, intermediate and long times via integrated photonics
• Ground-state blockade of Rydberg atoms and application in entanglement generation
• Quantum Computing in Plato's Cave
• Tomographically reconstructed master equations for any open quantum dynamics
• Dissipation-based entanglement via quantum Zeno dynamics and Rydberg antiblockade
• Measurement Induced Continuous Time Crystals
• On the combined use of GW approximation and cumulant expansion in the calculations of quasiparticle spectra: The paradigm of Si valence bands
• Zeno physics in ultrastrong circuit QED
• Quantum Zeno Dynamics through stochastic protocols
• Large fluctuations of the first detected quantum return time
• Quantum Zeno Dynamics from General Quantum Operations
• Fast and high-fidelity generation of steady-state entanglement using pulse modulation and parametric amplification
• Fidelity of fermionic atom-number states subjected to tunneling decay
• Non-Hermitian Dynamics in the Quantum Zeno Limit
• A nondestructive Bell-state measurement on two distant atomic qubits
• Constrained Optimization via Quantum Zeno Dynamics
• Operator Quantum Zeno Effect: Protecting Quantum Information with Noisy Two-Qubit Interactions
• Invariant-based inverse engineering for fluctuation transfer between membranes in an optomechanical cavity system
• Stochastic Quantum Zeno by Large Deviation Theory
• Preparation of entangled states through Hilbert space engineering
• Majoranas in Noisy Kitaev Wires
• Quantum Dynamics under continuous projective measurements: non-Hermitian description and the continuous space limit
• Generalized Adiabatic Theorem and Strong-Coupling Limits
• Non-Hermitian scattering on a tight-binding lattice
• Quantum Zeno effect and dynamics
• Accelerated and noise-resistant generation of a high-fidelity steady-state entanglement with Rydberg atoms
• Using the Quantum Zeno Effect for Suppression of Decoherence
• One bound to rule them all: from Adiabatic to Zeno
• Electroencephalographic field influence on calcium momentum waves
• Demonstration of universal control between non-interacting qubits using the Quantum Zeno effect
• Spin polarization recovery and Hanle effect for charge carriers interacting with nuclear spins in semiconductors
• Witnessing quantum coherence in the presence of noise
• Measurement-Induced Phase Transition in a Quantum Spin System
• Hadamard magnetization transfers achieve dramatic sensitivity enhancements in homonuclear multidimensional NMR correlations of labile sites in proteins, polysaccharides and nucleic acids
• Quantum Zeno effects across a parity-time symmetry breaking transition in atomic momentum space
• A quantum particle in a box with moving walls
• Obtaining pure steady states in nonequilibrium quantum systems with strong dissipative couplings
• Experimental proof of Quantum Zeno-assisted Noise Sensing
• Quantum nonreciprocal interactions via dissipative gauge symmetry
• Decoherence control in different environments
• Spread complexity for measurement-induced non-unitary dynamics and Zeno effect
• Quantum Zeno and Anti-Zeno probes of noise correlations in photon polarisation
• Quantum Zeno Subspaces induced by Temperature
• Universal scheme for indirect quantum control
• Analysis of the quantum Zeno effect for quantum control and computation
• Criterion for quantum Zeno and anti-Zeno effects
• Quantum simulation of non-Markovianity using the quantum Zeno effect
• Enhanced observability of quantum post-exponential decay using distant detectors
• Engineering Many-Body Dynamics with Quantum Light Potentials and Measurements
• Driving quantum systems with repeated conditional measurements
• Superradiance paradox in waveguide lattices
• Coherent control in quantum open systems: An approach for accelerating dissipation-based quantum state generation
• Measurement-Assisted Quantum Communication in Spin Channels with Dephasing
• Quantum Control with Measurements and Quantum Zeno Dynamics
• Stirring by Staring: Measurement Induced Chirality
• Quantum calcium-ion interactions with EEG
• Nonequilibrium work and entropy production by quantum projective measurements
• Quantum Zeno effect with partial measurement and noisy dynamics
• Uncertainty and symmetry bounds for the quantum total detection probability
• Linear and nonlinear Zeno effects in an optical coupler
• Quantum Zeno suppression of three-body losses in Bose-Einstein condensates
• Experimental test of the time stability of the half-life of alpha-decay Po-214 nuclei
• Noise Sensing via Stochastic Quantum Zeno
• Zeno dynamics in wave-packet diffraction spreading
• Beyond Zeno: Approaching Infinite Temperature upon Repeated Measurements
• Polaron dynamics and decoherence in an interacting two-spin system coupled to optical phonon environment
• Freezing Optical Rogue Waves by Zeno Dynamics
• Analytical study of quadratic and non-quadratic short-time behavior of quantum decay
• Non-Markovianity during quantum Zeno effect
• Improving the precision of frequency estimation via long-time coherences
• Quantum bath engineering of a high impedance microwave mode through quasiparticle tunneling
• Linear feedback stabilization of a dispersively monitored qubit
• Quantum Zeno effect for open quantum systems
• Stroboscopic observation of quantum many-body dynamics
• Transmission of classical and quantum information through a quantum memory channel with damping
• Quantum Brownian motion under generalized position measurements: A converse Zeno scenario
• Eternal Adiabaticity
• Coalescence of non-Markovian dissipation, quantum Zeno effect and non-Hermitian physics, in a simple realistic quantum system
• Non-Abelian Phases from a Quantum Zeno Dynamics
• Capturing non-exponential dynamics in the presence of two decay channels
• Simulating Zeno physics by quantum quench with superconducting circuits
• Universal Control Induced by Noise
• Retrodictive derivation of the radical-ion-pair master equation and Monte-Carlo simulation with single-molecule quantum trajectories
• Continuous measurements for control of superconducting quantum circuits
• Quantum Quasi-Zeno Dynamics: Transitions mediated by frequent projective measurements near the Zeno regime
• Quantum Zeno effect under continuous spin noise measurement in a quantum dot-micropillar cavity
• Quantum Zeno Effect of General Quantum Operations
• The effect of measurements, randomly distributed in time, on quantum systems. Stochastic quantum Zeno effect
• Targeting pure quantum states by strong noncommutative dissipation
• Unification of Random Dynamical Decoupling and the Quantum Zeno Effect
• Thermalization processes induced by quantum monitoring in multi-level systems
• Tunneling in Polymer Quantization and the Quantum Zeno Effect
• Quantum Zeno effect generalized
• Non-Hermitian and Zeno limit of quantum systems under rapid measurements
• Conditioned quantum motion of an atom in a continuously monitored 1D lattice
• The Role of Temperature in the occurrence of some Zeno Phenomena
• Variational approach to the dynamics of dissipative quantum impurity models
• Multichannel decay law
• Spin-helix states in the $XXZ$ spin chain with strong dissipation
• A Multi-Qubit Quantum Gate Using the Zeno Effect
• Noise-induced distributed entanglement in atom-cavity-fiber system
• KAM-Stability for Conserved Quantities in Finite-Dimensional Quantum Systems
• Optimal Measurement Protocols in Quantum Zeno Effect
• Overcoming Quantum Metrology Singularity through Sequential Measurements
• Results of a search for daily and annual variations of the Po-214 half-life at the two year observation period
• Protective Measurement -- a new quantum measurement paradigm: detailed description of the first realisation
• Protecting subspaces by acting on the outside
• Zeno subspace in quantum-walk dynamics
• Decoherence factor as a convolution: an interplay between a Gaussian and an exponential coherence loss
• Sources of the systematic errors in measurements of Po-214 decay half-life time variations at the Baksan deep underground experiments
• Quantum simulating the electron transport in quantum cascade laser structures
• Full decoherence induced by local fields in open spin chains with strong boundary couplings
• Optimal Zeno Dragging for Quantum Control: A Shortcut to Zeno with Action-based Scheduling Optimization
• A dynamical composition law for boundary conditions
• Non-exponential tunneling ionization of atoms by an intense laser field
• Optical measurement of electron spins in quantum dots: Quantum Zeno effects
• Uncertainty relation between detection probability and energy fluctuations
• Entropy of quantum states
• Optimal convergence rate in the quantum Zeno effect for open quantum systems in infinite dimensions
• Nonexponential decay of Feshbach molecules
• Measuring geometric phases with a dynamical quantum Zeno effect in a Bose-Einstein condensate
• Hamiltonian Purification
• Zeno Dynamics of Quantum Chirps
• Quantization of the mean decay time for non-Hermitian quantum systems
• Quantum State Reduction by Matter-Phase-Related Measurements in Optical Lattices
• Note on a Product Formula Related to Quantum Zeno Dynamics
• Generalized Product Formulas and Quantum Control
• Advances in sequential measurement and control of open quantum systems
• Macroscopic Zeno effect in Su-Schrieffer-Heeger photonic topological insulator
• Zeno effect of the open quantum system in the presence of 1/f noise
• Detecting ground state qubit self-excitations in circuit QED: slow quantum anti-Zeno effect
• Information-Probabilistic description of the Universe
• Large-time limit of the quantum Zeno effect
• Quantum cavities with alternating boundary conditions
• Energy fluctuation relations and repeated quantum measurements
• Grover Speedup from Many Forms of the Zeno Effect
• Classical limit of the quantum Zeno effect
• Classical Limit of the Quantum Zeno Effect by Environmental Decoherence
• The quantum Zeno and anti-Zeno effects: from weak to strong system-environment coupling
• Generation of polarization entanglement via the quantum Zeno effect
• Exceptional points and quantum correlations in precise measurements
• Quantum Zeno-based control mechanism for molecular fragmentation
• The Lee model: a tool to study decays
• The influence of the symmetry of identical particles on flight times
• Continuous Monitoring of Dynamical Systems and Master Equations
• Entangling non planar molecules via inversion doublet transition with negligible spontaneous emission
• Decoherence dynamics in molecular qubits: Exponential, Gaussian and beyond
• Thermodynamics and Protection of Discrete-Time Crystals
• On Strong Bounds for Trotter and Zeno Product Formulas with Bosonic Applications
• Tuning the nuclei-induced spin relaxation of localized electrons by the quantum Zeno and anti-Zeno effects
• Observation of partial and infinite-temperature thermalization induced by repeated measurements on a quantum hardware
• Hilbert space partitioning for non-Hermitian Hamiltonians: From off-resonance to Zeno subspaces
• Observing Quantum Trajectories: From Mott's Problem to Quantum Zeno Effect and Back
• State engineering of Bose-Einstein condensate in the optical lattice by a periodic sublattice of dissipative sites
• Zeno Dynamics for Open Quantum Systems
• Quantum control for the Zeno effect with noise
• Quantum Zeno effect: Quantum shuffling and Markovianity
• Generators of nonclassical states by combination of the linear coupling of boson modes, Kerr nonlinearity and the strong linear losses
• Optimising finite-time quantum information engines using Pareto bounds
• Kick and fix: the roots of quantum control
• Unraveling the switching dynamics in a quantum double-well potential
• Driving-induced population trapping and linewidth narrowing via the quantum Zeno effect
• Product formulas in the framework of mean ergodic theorems
• Probing False Vacuum Decay and Bubble Nucleation in a Rydberg Atom Array
• Quantum Zeno and anti-Zeno effects in surface diffusion of interacting adsorbates
• Ultrastrong coupling, nonselective measurement and quantum Zeno dynamics
• Electromagnetism in terms of quantum measurements
• Enhanced quantum tunneling in quantum Zeno dynamics freezing momentum direction
• Extraction of a squeezed state in a field mode via repeated measurements on an auxiliary quantum particle
• Out-of-equilibrium quantum dynamics of fermionic gases in the presence of localized particle loss
• Operational work fluctuation theorem for open quantum systems
• Bath Dynamical Decoupling with a Quantum Channel
• Perfectly absorbed and emitted currents by complex potentials in nonlinear media
• Optimal quantum transport on a ring via locally monitored chiral quantum walks
• Quantum Zeno effect in a multilevel molecule
• Using a biased qubit to probe complex systems
• Combinatorial Approach to Modeling Quantum Systems
• Adiabatic manipulation of a system interacting with a spin-bath
• Memory effects induced by initial switching conditions
• Motion from Measurement: The Role of Symmetry of Quantum Measurements
• Error metric for non-trace-preserving quantum operations
• Non-Hermitian interaction of a discrete state with a continuum
• Thwarted dynamics by partial projective measurements
• Lindbladian purification
• Quantum information processing with nuclear spins mediated by a weak-mechanically controlled electron spin
• Decay rates and decoherence of an interstitial two-level spin impurity in a ferromagnetic lattice
• Pinned QMA: The power of fixing a few qubits in proofs
• On the possibility to observe relations between quantum measurements and the entropy of phase transitions in Zn${}_2$(BDC)${}_2$(DABCO)
• Tunable Tradeoff between Quantum and Classical Computation via Nonunitary Zeno-like Dynamics
• Analysis of quantum decay law: Is quantum tunneling really exponential?
• Sensing microscopic noise events by frequent quantum measurements
• The semiclassical limit of a quantum Zeno dynamics
• Quantum Zeno Dynamics of Two Interacting Particles
• Truncated quantum observables and their semiclassical limit
• Eluding Zeno effect via dephasing and detuning
• Recovering optimal precision in quantum sensing with time domain imperfections
• The geometry of the quantum Zeno effect
• Quantum Zeno blockade in optomechanical systems
• From Krylov Complexity to Observability: Capturing Phase Space Dimension with Applications in Quantum Reservoir Computing
• Quantum Point Contact with Local Two-body Loss
• Extracting filtered signal statistics of continuously measured quantum systems
• Two-exponential decay of Acridine Orange
• Nonperturbative quantum theory of multiplasmonic electron emission from surfaces: Gauge-specific cumulant expansions vs. Volkov ansatz over plasmonic coherent states
• Evanescent Wave Approximation for Non-Hermitian Hamiltonians
• Nonlinear Zeno dynamics due to atomic interactions in Bose-Einstein condensate
• Unitary time-evolution in stochastic time-dependent Hilbert spaces
• Higher-order Zeno sequences
• Phenomenological quantum mechanics: I. Phenomenology of quantum observables
• Efficient Auxiliary-Field Quantum Monte Carlo using Isometric Tensor Hypercontraction
• A Testable Theory for The Emergence of the Classical World
• Localized states in monitored quantum walks
• Chernoff's product formula: Semigroup approximations with non-uniform time intervals
• Quantifying non-Hermiticity using single- and many-particle quantum properties
• Vacuum state truncation via the quantum Zeno effect
• Zeno Dynamics and High-Temperature Master Equations Beyond Secular Approximation
• Laser trapping of ions and asymptotic minimization of Decoherence
• Quantum Transition Rates in Arbitrary Physical Processes
• Modulator-Assisted Zeno Control of Energy Transfer in Quantum Batteries
• Theory of the correlated quantum Zeno effect in a monitored qubit dimer
• Violation of the "information-disturbance relationship" in finite-time quantum measurements
• Central Charge in Quantum Optics