Time-optimal quantum transformations with bounded bandwidth

Abstract

In this paper, we derive sharp lower bounds, also known as quantum speed limits, for the time it takes to transform a quantum system into a state such that an observable assumes its lowest average value. We assume that the system is initially in an incoherent state relative to the observable and that the state evolves according to a von Neumann equation with a Hamiltonian whose bandwidth is uniformly bounded. The transformation time depends intricately on the observable's and the initial state's eigenvalue spectrum and the relative constellation of the associated eigenspaces. The problem of finding quantum speed limits consequently divides into different cases requiring different strategies. We derive quantum speed limits in a large number of cases, and we simultaneously develop a method to break down complex cases into manageable ones. The derivations involve both combinatorial and differential geometric techniques. We also study multipartite systems and show that allowing correlations between the parts can speed up the transformation time. In a final section, we use the quantum speed limits to obtain upper bounds on the power with which energy can be extracted from quantum batteries.

arXiv comment19 pages, 4 figures, links to references corrected, accepted in Quantum

References in corpus (28)

• Extractable work from ensembles of quantum batteries. Entanglement helps
• Maximal work extraction from quantum systems
• 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
• Quantum speed limits in open system dynamics
• Quantacell: Powerful charging of quantum batteries
• Quantum Brachistochrone
• Largest separable balls around the maximally mixed bipartite quantum state
• Generalized Geometric Quantum Speed Limits
• Quantum Coherence and Ergotropy
• Bounds on the capacity and power of quantum batteries
• Quantum speed limit for arbitrary initial states
• Time Optimal Unitary Operations
• Quantum brachistochrone curves as geodesics: obtaining accurate control protocols for time-optimal quantum gates
• Separable balls around the maximally mixed multipartite quantum states
• A short note on passivity, complete passivity and virtual temperatures
• Zermelo Navigation and a Speed Limit to Quantum Information Processing
• Experimental time-optimal universal control of spin qubits in solids
• Solution to the quantum Zermelo navigation problem
• Time-optimal navigation through quantum wind
• Quantum speed limits and optimal Hamiltonians for driven systems in mixed states
• Quantum Brachistochrone for Mixed States
• Zermelo Navigation in the Quantum Brachistochrone
• A general formulation of time-optimal quantum control and optimality of singular protocols
• Holonomy in Quantum Information Geometry
• The flag manifold as a tool for analyzing and comparing data sets

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• Tight lower bounds on the time it takes to generate a geometric phase
• Quantum speed limits for an open system in contact with a thermal bath
• Optimal Work Extraction from Finite-Time Closed Quantum Dynamics
• Quantum speed limit for observables from quantum asymmetry