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Quantum speed limit for qubit systems: Exact results
Zhang, Lin1; Sun, Yuan2,3; Luo, Shunlong2,3
Source PublicationPHYSICS LETTERS A
AbstractGiven an initial state, a target state, and a driving Hamiltonian, how fast can the initial state evolve into the target state according to the Schrochinger dynamics? This problem arises in a variety of contexts such as quantum computation, quantum control, and in particular, the problem of maximum information processing rate of quantum systems, and has been studied extensively due to its fundamental importance. In this paper, we purse further the study in the qubit case in which the particular structure admits stronger results. We use the quantum fidelity as well as relative entropy as a figure of merit to characterize the closeness between a fixed initial qubit state and another one undergoing unitary evolution. We work out explicitly maximal and minimal fidelity and relative entropy by determining the closest and the farthest states to the target state and show that these results are unique for qubit systems. We also determine the minimal time for a state to evolve to the extremal states (that is, the farthest one evolved from the initial state in the sense of minimal fidelity or maximal relative entropy), which generalizes the celebrated Mandelstam-Tamm bound and the Margolus-Levitin bound for qubit systems. We further reveal an interesting fact that this minimal time is independent of the initial states. (C) 2018 Elsevier B.V. All rights reserved.
KeywordMandelstam-Tamm bound Margolus-Levitin bound Quantum speed limit Quantum fidelity Minimal evolution time
Funding ProjectZhejiang Provincial Natural Science Foundation[LY17A010027] ; NSFC[11301124] ; NSFC[61771174] ; cross-disciplinary innovation team building project of Hangzhou Dianzi University, National Natural Science Foundation of China[11375259] ; National Center for Mathematics and Interdisciplinary Sciences, CAS[Y029152K51]
WOS Research AreaPhysics
WOS SubjectPhysics, Multidisciplinary
WOS IDWOS:000442705300001
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Document Type期刊论文
Corresponding AuthorZhang, Lin; Sun, Yuan
Affiliation1.Hangzhou Dianzi Univ, Inst Math, Hangzhou 310018, Zhejiang, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Zhang, Lin,Sun, Yuan,Luo, Shunlong. Quantum speed limit for qubit systems: Exact results[J]. PHYSICS LETTERS A,2018,382(37):2599-2604.
APA Zhang, Lin,Sun, Yuan,&Luo, Shunlong.(2018).Quantum speed limit for qubit systems: Exact results.PHYSICS LETTERS A,382(37),2599-2604.
MLA Zhang, Lin,et al."Quantum speed limit for qubit systems: Exact results".PHYSICS LETTERS A 382.37(2018):2599-2604.
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