The Mandelstam-Tamm quantum speed limit puts a bound on how fast a closed system in a pure state can evolve. In this paper, we derive several extensions of this quantum speed limit to closed systems in mixed states. We also compare the strengths of these extensions and examine their tightness. The most widely used extension of the Mandelstam-Tamm quantum speed limit originates in Uhlmann’s energy dispersion estimate. We carefully analyze the underlying geometry of this estimate, an analysis that makes apparent that the Bures metric, or equivalently the quantum Fisher information, will rarely give rise to tight extensions. This observation leads us to address whether there is a tightest general extension of the Mandelstam-Tamm quantum speed limit. Using a geometric construction similar to that developed by Uhlmann, we prove that this is indeed the case. In addition, we show that tight evolutions of mixed states are typically generated by time-varying Hamiltonians, which contrasts with the case for systems in pure states.
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.