Quantum Speed Limits across the Quantum-to-Classical Transition

Shanahan, B.; Chenu, Aurélia; Margolus, Norman; Campo, Adolfo del

doi:10.1103/physrevlett.120.070401

Cited by 175 publications

(143 citation statements)

References 52 publications

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“…By introducing any kind of distance D(ρ(0), ρ(τ)) between density matrices, the triangle inequality gives  ò r r t t ( ( ) ( )) t g D d 0, tt 0 , where g tt is a metric on the space of density matrices induced by D [26]. By introducing the time-average as , we obtain the following formal inequality relation  t r r t á ñ t ( ( ) ( )) ( ) D g 0 , , 1 tt which is a geometric formulation of the QSL, and similar arguments apply to classical systems as well [16,17]. Note that equation (1) has been discussed for contractive Reimanninan metrics in [12] and for Shatten-p distances including the trace distance in [15].…”

Section: Introductionmentioning

confidence: 95%

Speed limit for open quantum systems

2019

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We study the quantum speed limit for open quantum systems described by the Lindblad master equation. The obtained inequality shows a trade-off relation between the operation time and the physical quantities such as the energy fluctuation and the entropy production. We further identify a quantity characterizing the speed of the state transformation, which appears only when we consider the open system dynamics in the quantum regime. When the thermal relaxation is dominant compared to the unitary dynamics of the system, we show that this quantity is approximated by the energy fluctuation of the counter-diabatic Hamiltonian which is used as a control field in the shortcuts to adiabaticity protocol. We discuss the physical meaning of the obtained quantum speed limit and try to give better intuition about the speed in open quantum systems. t .

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Section: Introductionmentioning

confidence: 95%

Speed limit for open quantum systems

2019

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“…Contrarily to what was initially believed, speed limits are not an exclusive property of quantum systems, namely they do not arise uniquely because of quantum features. Indeed, they can be derived also for classical systems, without assuming any quantum properties, such as commutation relations, as shown recently in [11,12].…”

Section: Introductionmentioning

confidence: 97%

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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“…For a comprehensive treatment and its history we refer to a recent Topical Review [26]. More recently, the quantum speed limit has found applications in a wide range of problems, including but not limited to metrology [27,28], quantum control [29][30][31], thermodynamics [32,33], and in studying the quantum to classical transition [34,35].…”

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confidence: 99%

Quantum speed limits and the maximal rate of information production

Deffner

2020

Phys. Rev. Research

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The Bremermann-Bekenstein bound sets a fundamental upper limit on the rate with which information can be processed. However, the original treatment heavily relies on cosmological properties and plausibility arguments. In the present analysis, we derive equivalent statements by relying on only two fundamental results in quantum information theory and quantum dynamics -Fannes inequality and the quantum speed limit. As main results, we obtain Bremermann-Bekenstein-type bounds for the rate of change of the von Neumann entropy in quantum systems undergoing open system dynamics, and for the rate of change of the Shannon information over some logical basis in unitary quantum evolution.

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Quantum Speed Limits across the Quantum-to-Classical Transition

Cited by 175 publications

References 52 publications

Speed limit for open quantum systems

Speed limit for open quantum systems

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

Quantum speed limits and the maximal rate of information production

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