The initial-state dependence of the quantum speed limit

Abstract

The generic bound of quantum speed limit time (the minimal evolution time) for a qubit system interacting with structural environment is investigated. We define a new bound for the quantum speed limit. It is shown that the non-Markovianity and the population of the excited state can fail to signal the quantum evolution acceleration, but the initial-state dependence is an important factor. In particular, we find that different quantum speed limits could produce contradictory predictions on the quantum evolution acceleration.

Quantum speed limit based on the bound of Bures angle

“…As the previous results in the Ref. [30,36], the evolution of the system will be accelerated not only in the non-Markovian regime but also in the Markovian regime when the initial state is not the excited state. And, we can observe that the quantum speed limit time reaches the maximum when γ 0 is in the vicinity of λ/2, and becomes shorter as the increasing of white noise.…”

“…Utilizing the Bures angle, Deffner and Lutz arrived a unified QSL bound for initial pure state, and showed that non-Markovian effects could speed up the quantum evolution [22]. Other forms of QSL in open system were also reported, such as the QSL in different environments [23][24][25][26][27][28][29], the initialstate dependence [30], the geometric form for Wigner phase space [31], the experimentally realizable metric [32]. In addition, many other aspects of QSL were also widely studied such as using the fidelity [33,34] and function of relative purity [35,36], the mechanism for quantum speedup [37], the connection with generation of quantumness [38], generalization of geometric QSL form [39], via gauge invariant distance [40], even the QSL for almost all states [41], and so on.…”

There is no general connection between the quantum speed limit and non-Markovianity

“…We are specifically interested in clarifying the connection between the QSL bound and the presence or absence of memory effects, described in terms of information backflow [13]. Following [4], this aspect has been further investigated, elaborating on the claim that the QSL is smaller when the dynamics is non-Markovian, potentially speeding up the evolution [14,15]. These authors showed analytically that, for a specific model of open quantum system dynamics, the ratio between the QSL and the actual evolution time, τ QSL /τ, is 1 when the system is Markovian, and is smaller…”

“…Their result suggests that in the Markovian case the dynamics saturates the bound, giving the most efficient evolution, whereas in the non-Markovian case the actual limit can still be lower than the evolution time. The explicitly derived dependency between QSL and non-Markovianity has proven useful in several applications [10,[15][16][17][18][19][20][21][22][23][24][25][26][27][28].Our main goal is to tackle the question of the connection between non-Markovianity and the QSL not starting from a specific model but in full generality, looking in detail at the role played by the dynamical map, the evolution time τ, and the initial state, in the achievement of the QSL bound. We show that, for the most general cases, there is no simple connection between the Markovian to non-Markovian crossover and the QSL.…”

Relationship between quantum speed limit time and memory time in a photonic-band-gap environment

“…Several new QSL time bounds for open quantum systems have been formulated8. The analysis of the environmental effects on the QSL time has been recently applied to a number of systems such as spin-boson models910, atoms in photonic crystals11, and spin chains12.…”