Generalized Geometric Quantum Speed Limits
Diego Paiva Pires, Marco Cianciaruso, Lucas C. Céleri, Gerardo Adesso, and Diogo O. Soares-Pinto
Phys. Rev. X 6, 021031 – Published 2 June 2016
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 nonuniqueness 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 that 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.
Received 21 July 2015
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Published by the American Physical Society
AUTHORS & AFFILIATIONS
Diego Paiva Pires1,*, Marco Cianciaruso2,3,4,†, Lucas C. Céleri5,‡, Gerardo Adesso2,§, and Diogo O. Soares-Pinto1,∥
1Instituto de Física de São Carlos, Universidade de São Paulo, CP 369, 13560-970 São Carlos, São Paulo, Brazil
2School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
3Dipartimento di Fisica “E. R. Caianiello,” Università degli Studi di Salerno, Via Giovanni Paolo II, I-84084 Fisciano (SA), Italy
4INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-84084 Fisciano (SA), Italy
5Instituto de Física, Universidade Federal de Goiás, 74.001-970 Goiânia, Goiás, Brazil
A fundamental question in physics pertains to how fast quantum states evolve. This so-called “quantum speed limit,” which corresponds to the minimum evolution time between two distinguishable states of a quantum system, is an important parameter for designing faster and more optimized information-processing machines. Here, we develop an elegant geometric formalism to provide general progress in the determination of quantum speed limits. This work unifies and improves previous findings and highlights, for the first time, the role of classical populations versus quantum coherences in the saturation of speed limits.
The new family of geometric quantum speed limits presented in this work is applicable to pure and mixed states and to all physical processes, both unitary and nonunitary (e.g., amplitude and phase damping). We express the quantum speed limits in terms of the shortest distance between two states in the quantum state space, according to different measures of distance. For any given dynamical process, the tightest speed limit can be determined by selecting the quantum metric that is most tailored to the initial state of a closed or open system.
Our results, which provide general prescriptions to optimize quantum protocols, pave the way for experimental demonstrations of controlled quantum dynamics operating at the ultimate speed limits using, for example, nuclear magnetic resonance technology. We expect that our findings will have an impact on the fields of quantum information, computation, simulation, and metrology.
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