Generalised quantum speed limit for arbitrary time-continuous evolution
arXiv:2207.04124 · doi:10.1088/1751-8121/ad15ad
Abstract
The quantum speed limit describes how quickly a quantum system can evolve in time from an initial state to a final state under a given dynamics. Here, we derive a generalised quantum speed limit (GQSL) for arbitrary time-continuous evolution using the geometrical approach of quantum mechanics. The GQSL is applicable for quantum systems undergoing unitary, non-unitary, completely positive, non-completely positive and relativistic quantum dynamics. This reduces to the well known standard quantum speed limit (QSL), i.e., the Mandelstam-Tamm bound when the quantum system undergoes unitary time evolution. Using our formalism, we then obtain a quantum speed limit for non-Hermitian quantum systems. To illustrate our findings, we have estimated the quantum speed limit for a time-independent non-Hermitian system as well as for a time-dependent non-Hermitian system namely the Bethe-Lamb Hamiltonian for general two-level system.
arXiv comment10 pages, 4 figures, close to published version
References in corpus (69)
- Complex Extension of Quantum Mechanics
- The maximum speed of dynamical evolution
- Quantum metrology from a quantum information science perspective
- Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
- The elusive Heisenberg limit in quantum enhanced metrology
- Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
- Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms
- 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
- Observation of parity-time symmetry breaking in a single spin system
- Faster than Hermitian Quantum Mechanics
- The fundamental limit on the rate of quantum dynamics: the unified bound is tight
- More bang for your buck: Towards super-adiabatic quantum engines
- Generalized Geometric Quantum Speed Limits
- Trade-off between speed and cost in shortcuts to adiabaticity
- Bounds on the capacity and power of quantum batteries
- Energy-time uncertainty relation for driven quantum systems
- Mixed-state evolution in the presence of gain and loss
- Geometric derivation of the quantum speed limit
- Dynamically encircling an exceptional point in a real quantum system
- Tightening Quantum Speed Limits for Almost All States
- Speed limit for open quantum systems
- Anti-Parity-Time Symmetric Optical Four-Wave Mixing in Cold Atoms
- Quantum Coherence Sets The Quantum Speed Limit For Mixed States
- Nonlinear quantum metrology of many-body open systems
- Unifying Quantum and Classical Speed Limits on Observables
- Precision thermometry and the quantum speed limit
- Speed limits for quantum gates in multi-qubit systems
- Observation of -symmetric quantum coherence in a single ion system
- Quantum Speed Limit For Mixed States Using Experimentally Realizable Metric
- Comment on "Geometric derivation of the quantum speed limit"
- Quantum speed limits and the maximal rate of information production
- On the Connection Between Entanglement and the Speed of Quantum Evolution
- Measuring Non-Hermitian Operators via Weak Values
- Quantum Speed Limit and optimal evolution time in a two-level system
- Entanglement and the Lower Bounds on the Speed of Quantum Evolution
- Quantum Speed Limit for States with a Bounded Energy Spectrum
- Optimized heat transfer at exceptional points in quantum circuits
- A generalization of Margolus-Levitin bound
- Tighter Uncertainty and Reverse Uncertainty Relations
- Quantum speed limits for information and coherence
- Quantum speed limits and optimal Hamiltonians for driven systems in mixed states
- Reverse Quantum Speed Limit: How Slow Quantum Battery can Discharge?
- Observing crossover between quantum speed limits
- Quantum Speed Limits for Observables
- Quantum speed limits on operator flows and correlation functions
- Quantum Speed Limits under Continuous Quantum Measurements
- Finite-Dimensional PT-Symmetric Hamiltonians
- Tight Upper Bound Of The Maximum Speed Of Evolution Of A Quantum State
- Entanglement and the Speed of Evolution in Mixed States
- Fundamental Speed Limits to the Generation of Quantumness
- Products of weak values: uncertainty relations, complementarity and incompatibility
- Geometric Operator Quantum Speed Limit, Wegner Hamiltonian Flow and Operator Growth
- Quantum speed limit constraints on a nanoscale autonomous refrigerator
- Complexity Functionals and Complexity Growth Limits in Continuous MERA Circuits
- Quantum correlations in -symmetric systems
- Time scaling and quantum speed limit in non-Hermitian Hamiltonians
- Speed limits on correlations in bipartite quantum systems
- Capacity of Entanglement for Non-local Hamiltonian
- Information retrieval and eigenstates coalescence in a non-Hermitian quantum system with anti- symmetry
- Physical time-energy cost of a quantum process determines its information fidelity
- Uncertainty relation of Anandan-Aharonov and Intelligent states
- Strong unitary uncertainty relations
- Bounds to unitary evolution
- Time-Energy Measure for Quantum Processes
- Fundamental Limits on the Speed of Evolution of Quantum States
- Limits to Perception by Quantum Monitoring with Finite Efficiency
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- Energetic cost for speedy synchronization in non-Hermitian quantum dynamics
- Quantum Speed Limits Based on Schatten Norms: Universality and Tightness
- A geometrical description of non-Hermitian dynamics: speed limits in finite rank density operators
- Family of Exact and Inexact Quantum Speed Limits for Completely Positive and Trace-Preserving Dynamics
- Three perspectives on entropy dynamics in a non-Hermitian two-state system
- Generalized Entropic Quantum Speed Limits
- Probing the quantum speed limit and entanglement in flavor oscillations of neutrino-antineutrino system in curved spacetime
- Propagation-Distance Limit for a Classical Nonlocal Optical System
- Influence of gravity on the quantum speed limit in neutrino oscillations
- A unified fidelity-based framework for quantum speed limits in open quantum systems