Tight, robust, and feasible quantum speed limits for open dynamics

Abstract

Starting from a geometric perspective, we derive a quantum speed limit for arbitrary open quantum evolution, which could be Markovian or non-Markovian, providing a fundamental bound on the time taken for the most general quantum dynamics. Our methods rely on measuring angles and distances between (mixed) states represented as generalized Bloch vectors. We study the properties of our bound and present its form for closed and open evolution, with the latter in both Lindblad form and in terms of a memory kernel. Our speed limit is provably robust under composition and mixing, features that largely improve the effectiveness of quantum speed limits for open evolution of mixed states. We also demonstrate that our bound is easier to compute and measure than other quantum speed limits for open evolution, and that it is tighter than the previous bounds for almost all open processes. Finally, we discuss the usefulness of quantum speed limits and their impact in current research.

arXiv commentMain: 11 pages, 3 figures. Appendix: 2 pages, 1 figure

References in corpus (61)

• Advances in Quantum Metrology
• Ultimate physical limits to computation
• The role of quantum information in thermodynamics --- a topical review
• The maximum speed of dynamical evolution
• The elusive Heisenberg limit in quantum enhanced metrology
• Quantum Metrology in Non-Markovian Environments
• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Enhancing the charging power of quantum batteries
• Quantum speed limit for physical processes
• Quantum speed limit for non-Markovian dynamics
• Optimal Control at the Quantum Speed Limit
• Quantum speed limits in open system dynamics
• Universal Quantum Estimator
• Direct estimations of linear and non-linear functionals of a quantum state
• Quantum limits to dynamical evolution
• The fundamental limit on the rate of quantum dynamics: the unified bound is tight
• Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model
• Characterization of the Positivity of the Density Matrix in Terms of the Coherence Vector Representation
• The problem with the geometric discord
• Quantum speed limits, coherence and asymmetry
• Generalized Geometric Quantum Speed Limits
• Trade-off between speed and cost in shortcuts to adiabaticity
• Driving at the quantum speed limit: Optimal control of a two-level system
• Quantum Metrology in Open Systems: Dissipative Cramér-Rao Bound
• Monotonically convergent optimization in quantum control using Krotov's method
• A New Approach to Collaborative Filtering: Operator Estimation with Spectral Regularization
• Qubit-oscillator dynamics in the dispersive regime: analytical theory beyond rotating-wave approximation
• Energy-time uncertainty relation for driven quantum systems
• Shortcuts to adiabaticity by counterdiabatic driving for trapped-ion displacement in phase space
• Estimating the spectrum of a density operator
• Quantum Speed Limits Across the Quantum-to-Classical Transition
• Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise
• Quantum Speed Limit is Not Quantum
• Universal Work Fluctuations during Shortcuts To Adiabaticity by Counterdiabatic Driving
• Tightening Quantum Speed Limits for Almost All States
• Continuous Monitoring of Rabi Oscillations in a Josephson Flux Qubit
• Classical and Quantum Fisher Information in the Geometrical Formulation of Quantum Mechanics
• Contractivity of positive and trace preserving maps under $L_p$ norms
• Communication at the quantum speed limit along a spin chain
• Superadiabatic Controlled Evolutions and Universal Quantum Computation
• Quantum brachistochrone curves as geodesics: obtaining accurate control protocols for time-optimal quantum gates
• Quantum Coherence Sets The Quantum Speed Limit For Mixed States
• Quantum Speed Limit Bounds in an Open Quantum Evolution
• Shortcut to adiabatic gate teleportation
• Quantum Speed Limit For Mixed States Using Experimentally Realizable Metric
• Experimental time-optimal universal control of spin qubits in solids
• Time-dependent Hamiltonians with 100% evolution speed efficiency
• Tomographically reconstructed master equations for any open quantum dynamics
• Speed limits in Liouville space for open quantum systems
• Quantum Speed Limits under Continuous Quantum Measurements
• Generalized Shortcuts to Adiabaticity and Enhanced Robustness Against Decoherence
• Quantum Speed Limits for Quantum Information Processing Tasks
• Experimental Implementation of Generalized Transitionless Quantum Driving
• Control of open quantum systems: Case study of the central spin model
• Entanglement and the Speed of Evolution in Mixed States
• An improved bound for quantum speed limit time in open quantum systems by introducing an alternative fidelity
• Energetics of correlations in interacting systems
• The roles of drift and control field constraints upon quantum control speed limits
• Lazy states: sufficient and necessary condition for zero quantum entropy rates under any coupling to the environment
• Dependence of the Quantum Speed Limit on System Size and Control Complexity
• Distinguishability times and asymmetry monotone-based quantum speed limits in the Bloch ball

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• Operational definition of a quantum speed limit
• From quantum speed limits to energy-efficient quantum gates
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• Bounding generalized relative entropies: Nonasymptotic quantum speed limits
• Quantum coherence and speed limit in the mean-field Dicke model of superradiance
• Thermodynamics and the quantum speed limit in the non-Markovian regime
• An algorithm for solving unconstrained unitary quantum brachistochrone problems
• Quantum speed limit for robust state characterization and engineering
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• Quantum speed limit helps interpret geometric measure of entanglement
• Experimental Investigation of Geometric Quantum Speed Limits in an Open Quantum System
• Tight and attainable quantum speed limit for open systems
• Bhatia-Davis formula in the quantum speed limit
• Extreme depolarization for any spin
• Analysis of lower bounds for quantum control times and their relation to the quantum speed limit
• Optimizing performance of quantum operations with non-Markovian decoherence: the tortoise or the hare?
• Quantum speed limit of a noisy continuous-variable system
• Quantum Speed Limit in Terms of Coherence Variations
• Quantum speed limit of Jaynes-Cummings model with detuning for arbitrary initial states
• Fundamental speed limits on entanglement dynamics of bipartite quantum systems
• Classical and quantum speed limits
• Quantum Speed Limits Based on Schatten Norms: Universality and Tightness
• Bounds on the breaking time for entanglement-breaking channels
• Purity Speed Limit of Open Quantum Systems from Magic Subspaces
• Quantum speed of evolution in a Markovian bosonic environment
• Family of Exact and Inexact Quantum Speed Limits for Completely Positive and Trace-Preserving Dynamics
• The effect of Homodyne-based feedback control on quantum speed limit time
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• Laser-field detuning assisted optimization of exciton valley dynamics in monolayer WSe${}_2$: Geometric quantum speed limit
• Quantum speed limit and stability of coherent states in quantum gravity
• Family of attainable geometric quantum speed limits
• Quantum speed limit time in relativistic frame
• Hamiltonian quantum gates -- energetic advantage from entangleability
• Quantum speed limits in dephasing dynamics of a qubit system coupled to thermal environments
• Attainable quantum speed limit for N-dimensional quantum systems
• Effect of measurements on quantum speed limit
• PT symmetry and the evolution speed in open quantum systems
• Quantum Transition Rates in Arbitrary Physical Processes
• Implementation of multiparticle quantum speed limits on observables
• Tight bounds of quantum speed limit for noisy dynamics via maximum rotation angles
• A unified fidelity-based framework for quantum speed limits in open quantum systems
• Information Processing in Quantum Thermodynamic Systems: an Autonomous Hamiltonian Approach
• Trajectory-independent speed limits for controlled open quantum systems