Quantum Speed Limits Based on Schatten Norms: Universality and Tightness

Abstract

We discuss quantum speed limits (QSLs) for finite-dimensional quantum systems undergoing general physical processes. These QSLs were obtained using Schatten $\alpha$-norms, firstly exploiting geometric features of the quantum state space, and secondly by applying the Holder's inequality for matrix norms. For single-qubit states, we find that the geometric QSL is independent of the chosen Schatten norm, thus revealing universality behavior. We compare these QSLs with existing speed limits in literature, showing that the latter results represent particular cases of a general class of QSLs related to Schatten $\alpha$-norms. We address necessary and sufficient conditions for the tightness of the QSLs that depends on populations and coherences of the qubits, also addressing their geometric meaning. We compare the QSLs obtained for qubit dynamics, also exploring their geometrical meaning. Finally, we show that the geometric QSL is tighter for general qubit dynamics with initial pure states, which indicates a universal QSL.

References in corpus (51)

• Advances in Quantum Metrology
• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Observable measure of quantum coherence in finite dimensional systems
• 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
• Quantum limits to dynamical evolution
• The fundamental limit on the rate of quantum dynamics: the unified bound is tight
• Generalized Clausius inequality for nonequilibrium quantum processes
• Bounds on the capacity and power of quantum batteries
• Energy-time uncertainty relation for driven quantum systems
• Geometric derivation of the quantum speed limit
• Quantum Speed Limits Across the Quantum-to-Classical Transition
• Quantum Speed Limit is Not Quantum
• Speed limit for open quantum systems
• Geometrical Bounds of the Irreversibility in Markovian Systems
• Quantum Coherence Sets The Quantum Speed Limit For Mixed States
• Orthogonality Catastrophe as a Consequence of the Quantum Speed Limit
• Unifying Quantum and Classical Speed Limits on Observables
• Tight, robust, and feasible quantum speed limits for open dynamics
• Quantum Speed Limit Bounds in an Open Quantum Evolution
• The role of entanglement in dynamical evolution
• Geometric quantum speed limits: a case for Wigner phase space
• On the Connection Between Entanglement and the Speed of Quantum Evolution
• Comment on "Geometric derivation of the quantum speed limit"
• Statistical speed of quantum states: Generalized quantum Fisher information and Schatten speed
• Action quantum speed limits
• Unifying speed limit, thermodynamic uncertainty relation and Heisenberg principle via bulk-boundary correspondence
• Quantum Speed Limit for States with a Bounded Energy Spectrum
• Probing Quantum Speed Limits with Ultracold Gases
• Bounds in Nonequilibrium Quantum Dynamics
• Reverse Quantum Speed Limit: How Slow Quantum Battery can Discharge?
• Quantum Speed Limits for Observables
• Role of non-Markovianity and backflow of information in the speed of quantum evolution
• There is no general connection between the quantum speed limit and non-Markovianity
• Kibble-Zurek scaling in quantum speed limits for shortcuts to adiabaticity
• Quantum Evolution Time Limit: a General Non-Markovian Bound
• Extensions of the Mandelstam-Tamm quantum speed limit to systems in mixed states
• Bounding generalized relative entropies: Nonasymptotic quantum speed limits
• Thermodynamic speed limits for mechanical work
• Quantum speed limit for robust state characterization and engineering
• Margolus-Levitin quantum speed limit for an arbitrary fidelity
• Speed limits of the trace distance for open quantum system
• Generalised quantum speed limit for arbitrary time-continuous evolution
• Minimal time required to charge a quantum system
• Experimental Investigation of Geometric Quantum Speed Limits in an Open Quantum System
• Tight and attainable quantum speed limit for open systems
• Quantum speed limit and divisibility of the dynamical map
• Estimating the time evolution of NMR systems via quantum speed limit-like expression
• Closed systems refuting quantum-speed-limit hypotheses

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