Revealing memory effects in phase-covariant quantum master equations

Teittinen, Jose; Lyyra, Henri; Sokolov, Boris; Maniscalco, Sabrina

doi:10.1088/1367-2630/aacc38

Cited by 32 publications

(51 citation statements)

References 48 publications

(102 reference statements)

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“…measure. For more details see [35]. By comparing figures 7 and 8, we notice that the points where the τ QSL /τ changes dramatically in figure 7 coincides with the transition between Markovian and non-Markovian dynamics in figure 8.…”

Section: Eternal Non-markovianitymentioning

confidence: 69%

“…Multiple colors indicate that the non-Markovian region is represented by the union of these colors. For more details see [35].…”

Section: Discussionmentioning

confidence: 99%

“…The example dynamics considered in this paper arise from two very general families of master equations, namely the phase-covariant master equation [32][33][34][35][36]: 3 1 2 3 3 3 and the Pauli master equation [37,38]:…”

Section: Qsl Non-markovianity and Open Quantum Systemsmentioning

confidence: 99%

“…As an example, we use the phase-covariant system of equation (3) which does not increase coherences between | ñ 0 and | ñ 1 [35]. For the commutative class of phase-covariant dynamics 4 , that is when γ 1 (t)=γ(t) and γ 2 (t)=κγ(t), with k   0 1, the functions g(t) and h(t) have the form…”

Section: Example: Phase-covariant Commutative Dynamicsmentioning

confidence: 99%

“…Thus, violation of ( ) ( ) + +  t t 1 4 cos sin 0 implies τ QSL /τ<1. According to [35], this dynamical map is BLP non-Markovian if and only if γ 1 (t)+γ 2 (t)+4γ 3 (t)<0 which in this case is equivalent to ( ) ( ) + + < t t 1 4 cos sin 0. So, we see that for a=1/2 BLP non-Markovianity begins exactly at the same time as τ QSL /τ starts to decrease.…”

Section: Eternal Non-markovianitymentioning

confidence: 99%

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

2019

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The quantum speed limit (QSL) sets a bound on the minimum time required for a quantum system to evolve between two states. For open quantum systems this quantity depends on the dynamical map describing the time evolution in presence of the environment, on the evolution time τ, and on the initial state of the system. We consider a general single qubit open dynamics and show that there is no simple relationship between memory effects and the tightness of the QSL bound. We prove that only for specific classes of dynamical evolutions and initial states, there exists a link between non-Markovianity and the QSL. Our results shed light on the connection between information back-flow between system and environment and the speed of quantum evolution. than 1 when it is non-Markovian. 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. Under certain more restrictive assumptions, however, we can characterize families of one-qubit dynamical maps for which the QSL speed-up coincides with the onset of non-Markovianity, as indicated by the Breuer-Laine-Piilo (BLP) non-Markovianity measure [13]. For these families we derive analytical formulas for the QSL as a function of the BLP measure. Our results also show that, for a given open quantum system model, both the evolution time τ and the initial state play a key role and cannot be overlooked when making claims on the QSL. As an example, we generalize results in [4] to a broader set of pure initial states, and show that the QSL bound is saturated only for very few initial states even in the fully Markovian case.The paper is structured as follows. In section 2 we briefly present the formalism of open quantum systems and recall the common mathematical definitions of QSL. In section 3 we present the Jaynes-Cummings (JC) model used in [4] and discuss briefly their results concerning non-Markovianity and quantum speed-up. In section 4 we study how the actual evolution time affects the QSL for the same JC system. In section 5, we calculate the general conditions for the QSL optimal dynamics, and study the connection between BLP non-Markovianity and QSL. In section 6 we study the initial state dependence of the QSL for the Markovian dynamics arising from Pauli and phase-covariant master equations. In section 7 we study the effects of Markov...

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Section: Eternal Non-markovianitymentioning

confidence: 69%

“…Multiple colors indicate that the non-Markovian region is represented by the union of these colors. For more details see [35].…”

Section: Discussionmentioning

confidence: 99%

Section: Qsl Non-markovianity and Open Quantum Systemsmentioning

confidence: 99%

Section: Example: Phase-covariant Commutative Dynamicsmentioning

confidence: 99%

Section: Eternal Non-markovianitymentioning

confidence: 99%

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

2019

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Phase Covariant Channel: Quantum Speed Limit of Evolution

2022

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The quantum speed of evolution for the phase covariant map is investigated. This involves absorption, emission, and dephasing processes. The maps under various combinations of the above processes are considered to investigate the effect of phase covariant maps on quantum speed limit time. For absorption-free phase covariant maps, combinations of dissipative and CP-(in)divisible (non)-Markovian dephasing noises are considered. The role of coherence-mixedness balance on the speed limit time is checked in the presence of both vacuum and finite temperature effects. The rate at which Holevo's information changes and the action quantum speed of evolution for specific cases of the phase covariant map are also investigated.

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Non-monotonic Population and Coherence Evolution in Markovian Open-System Dynamics

Haase

Smirne

Huelga

2019

Springer Proceedings in Physics

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We consider a simple microscopic model where the open-system dynamics of a qubit, despite being Markovian, shows features which are typically associated to the presence of memory effects. Namely, a non monotonic behavior both in the population and in the coherence evolution arises due to the presence of non-secular contributions, which break the phase covariance of the Lindbladian (semigroup) dynamics. We also show by an explicit construction how such a non-monotonic behaviour can be reproduced by a phase covariant evolution, but only at the price of inserting some state-dependent memory effects.

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Revealing memory effects in phase-covariant quantum master equations

Cited by 32 publications

References 48 publications

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

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

Phase Covariant Channel: Quantum Speed Limit of Evolution

Non-monotonic Population and Coherence Evolution in Markovian Open-System Dynamics

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