Generalized Geometric Quantum Speed Limits

Abstract

The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the non uniqueness of a bona fide measure of distinguishability defined on the quantum state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits, and provides instances of novel bounds which are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.

17 pages, 8 figures. Close to published version

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Cited by in corpus (168)

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• Quantum Speed Limit is Not Quantum
• Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits
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• Stochastic thermodynamic interpretation of information geometry
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• Autonomous quantum clocks: does thermodynamics limit our ability to measure time?
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• Quantum metrology with full and fast quantum control
• Geometrical Bounds of the Irreversibility in Markovian Systems
• Fisher Information in Noisy Intermediate-Scale Quantum Applications
• Stochastic time-evolution, information geometry and the Cramer-Rao Bound
• Quantum Coherence Sets The Quantum Speed Limit For Mixed States
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• Orthogonality Catastrophe as a Consequence of the Quantum Speed Limit
• Estimation of Gaussian quantum states
• Unifying Quantum and Classical Speed Limits on Observables
• Geometric Speed Limit of Accessible Many-Body State Preparation
• Tight, robust, and feasible quantum speed limits for open dynamics
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• Entropic uncertainty relations for Markovian and non-Markovian processes under a structured bosonic reservoir
• Bounds on charging power of open quantum batteries
• Statistical speed of quantum states: Generalized quantum Fisher information and Schatten speed
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• Demonstration of quantum brachistochrones between distant states of an atom
• Probing Quantum Speed Limits with Ultracold Gases
• Thermodynamic uncertainty relation and thermodynamic speed limit in deterministic chemical reaction networks
• Tighter Uncertainty and Reverse Uncertainty Relations
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• Quantum Speed Limits for Observables
• Operational definition of a quantum speed limit
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• Quantum Speed Limits under Continuous Quantum Measurements
• Topological Speed Limit
• How difficult is it to prepare a quantum state?
• There is no general connection between the quantum speed limit and non-Markovianity
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• The roles of drift and control field constraints upon quantum control speed limits
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• Speed limits on correlations in bipartite quantum systems
• Non-equilibrium readiness and accuracy of Gaussian Quantum Thermometers
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• Extrapolating the thermodynamic length with finite-time measurements
• Exact zeros of the Loschmidt echo and quantum speed limit time for the dynamical quantum phase transition in finite-size systems
• Thermodynamics and the quantum speed limit in the non-Markovian regime
• Amplifying asymmetry with correlated catalysts
• Controlling decoherence speed limit of a single impurity atom in a Bose-Einstein-condensate reservoir
• Quantum Control in Open and Periodically Driven Systems
• Information geometry approach to quantum stochastic thermodynamics
• Margolus-Levitin quantum speed limit for an arbitrary fidelity
• Generalised quantum speed limit for arbitrary time-continuous evolution
• Taming quantum systems: A tutorial for using shortcuts-to-adiabaticity, quantum optimal control, and reinforcement learning
• Detecting quantum speedup in closed and open systems
• Tight and attainable quantum speed limit for open systems
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• Geometric approach to quantum statistical inference
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• Thermodynamic correlation inequality
• Impact of non-Markovian evolution on characterizations of quantum thermodynamics
• Quantum speed limit for states and observables of perturbed open systems
• Time-optimal quantum transformations with bounded bandwidth
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• Quantum Speed Limit in Terms of Coherence Variations
• Quantum speed limits in arbitrary phase spaces
• Quantum Speed Limit under Brachistochrone Evolution
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• Fundamental speed limits on entanglement dynamics of bipartite quantum systems
• Quantum Velocity Limits for Multiple Observables: Conservation Laws, Correlations, and Macroscopic Systems
• Classical and quantum speed limits
• Enhancing precision thermometry with nonlinear qubits
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• Measure of the density of quantum states in information geometry and its application in the quantum multi-parameter estimation
• Speed limits and thermodynamic uncertainty relations for quantum systems governed by non-Hermitian Hamiltonian
• Mixed states driven by Non-Hermitian Hamiltonians of a nuclear spin ensemble
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• Hybrid quantum-classical simulation of quantum speed limits in open quantum systems
• An improved bound for strong unitary uncertainty relations with refined sequence
• Fast Functionalization with High Performance in the Autonomous Information Engine
• Purity Speed Limit of Open Quantum Systems from Magic Subspaces
• Fermionic correlations as metric distances: a useful tool for materials science
• Optimal light cone for macroscopic particle transport in long-range systems: A quantum speed limit approach
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• Family of Exact and Inexact Quantum Speed Limits for Completely Positive and Trace-Preserving Dynamics
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• Quantum noise generated by local random Hamiltonians
• Information Geometric Aspects of Probability Paths with Minimum Entropy Production for Quantum State Evolution
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• Exact and lower bounds for the quantum speed limit in finite dimensional systems
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• Probing quantum phase transition via quantum speed limit
• Quantum dynamical speedup for correlated initial states
• Generalized Entropic Quantum Speed Limits
• Thermodynamic interpretation to Stochastic Fisher Information and Single-Trajectory Speed Limits
• Tighter Lower Bounds on Quantum Annealing Times
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• Coherent Quantum Speed Limits
• Quantum Speed Limits Based on the Sharma-Mittal Entropy
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• Holonomy in Quantum Information Geometry
• Operational Interpretation of Quantum Fisher Information in Quantum Thermodynamics
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• Thermodynamic speed limit for non-adiabatic work and its classical-quantum decomposition
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