Role of non-Markovianity and backflow of information in the speed of quantum evolution

Cianciaruso, Marco; Maniscalco, Sabrina; Adesso, Gerardo

doi:10.1103/physreva.96.012105

Cited by 41 publications

(35 citation statements)

References 61 publications

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“…We apply this finding to several recently introduced non-Markovianity indicators and we use this approach to make a comprehensive comparison of their sensitivity. Since our approach does not depend on the specification of the analytic form of the time-dependent decay rates, it can be applied in a variety of physical situations, such as those considered in [21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Revealing memory effects in phase-covariant quantum master equations

et al. 2018

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We study and compare the sensitivity of multiple non-Markovianity indicators for a qubit subjected to general phase-covariant noise. For each of the indicators, we derive analytical conditions to detect the dynamics as non-Markovian. We present these conditions as relations between the time-dependent decay rates for the general open system dynamics and its commutative and unital subclasses. These relations tell directly if the dynamics is non-Markovian w.r.t.each indicator, without the need to explicitly derive and specify the analytic form of the time-dependent coefficients. Moreover, with a shift in perspective, we show that if one assumes only the general form of the master equation, measuring the non-Markovianity indicators gives us directly non-trivial information on the relations between the unknown decay rates.

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Section: Introductionmentioning

confidence: 99%

Revealing memory effects in phase-covariant quantum master equations

et al. 2018

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“…Quantifiers of the statistical distance and speed of quantum states play an integral role in quantum information theory [10][11][12]. They are used to quantify the distinguishability of quantum states [10,11,13], to understand geometrical aspects of quantum mechanics and quantum phase transitions [12,[14][15][16][17][18][19][20][21][22][23], to quantify initial correlations, information flow * manuel.gessner@ino.it and non-Markovian effects in quantum evolutions [24][25][26][27], to determine the precision of phase estimation [1,3,5,28], to derive limits on the evolution time [29][30][31][32] or on the occurrence of quantum Zeno dynamics [33], and to quantify and detect quantum properties such as coherence [34], quantum correlations and discord [35][36][37][38], uncertainty [39], asymmetry [8,40], or purity [41,42].…”

Section: Introductionmentioning

confidence: 99%

Statistical speed of quantum states: Generalized quantum Fisher information and Schatten speed

Gessner

Smerzi

2018

Phys. Rev. A

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We analyze families of measures for the quantum statistical speed which include as special cases the quantum Fisher information, the trace speed, i.e., the quantum statistical speed obtained from the trace distance, and more general quantifiers obtained from the family of Schatten norms. These measures quantify the statistical speed under generic quantum evolutions and are obtained by maximizing classical measures over all possible quantum measurements. We discuss general properties, optimal measurements and upper bounds on the speed of separable states. We further provide a physical interpretation for the trace speed by linking it to an analog of the quantum Cramér-Rao bound for median-unbiased quantum phase estimation.

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“…In particular, bounds have been derived for the maximum speed of evolution under non-unitary dynamics almost simultaneously by Taddei et al [12], Del Campo et al [14] and Deffner and Lutz [13]. Special attention has been devoted to studying the predicted speed-up of the evolution in open systems undergoing non-Markovian dynamics [36][37][38][39]. Other important cases of study are QSLs for mixed states [40][41][42][43][44][45], the geometric characterization of the QSL [46][47][48][49] and its connection to parameter estimation theory [12,[50][51][52].…”

Section: Extensions and Other Studiesmentioning

confidence: 99%

Analysis of Lower Bounds for Quantum Control Times and Their Relation to the Quantum Speed Limit

Poggi¹

2020

AnAFA

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Las restricciones a la velocidad de evolución de un estado cuántico, usualmente llamadas "límite de velocidades cuántico" (QSL), presentan importantes consecuencias para problemas de control cuántico. Sin embargo, en su formulación usual, no es trivial obtener cotas inferiores tipo QSL para el tiempo de evolución en el caso de Hamiltonianos dependientes del tiempo con parámetros desconocidos. En este trabajo presentamos un introducción a la formulación del límite de velocidades cuántico para evolución unitaria y su conexión con control cuántico. Luego, analizamos nuevos métodos para obtener cotas inspiradas en el QSL para tiempos de evolución en problemas de control. Finalmente, extendemos el trabajo presentado en [Poggi, Lombardo and Wisniacki EPL 104 40005 (2013)] estudiando las propiedades y limitaciones de las cotas presentadas en un sistema de dos niveles.Palabras clave: información cuántica, control cuántico.Limitations to the speed of evolution of quantum systems, typically referred to as quantum speed limits (QSLs), have important consequences for quantum control problems. However, in its standard formulation, is not straightforward to obtain meaningful QSL bounds for time-dependent Hamiltonians with unknown control parameters. In this paper we present a short introductory overview of quantum speed limit for unitary dynamics and its connection to quantum control. We then analyze potential methods for obtaining new bounds on control times inspired by the QSL. We finally extend the work in [Poggi, Lombardo and Wisniacki EPL 104 40005 (2013)] by studying the properties and limitations of these new bounds in the context of a driven two-level quantum system.

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Role of non-Markovianity and backflow of information in the speed of quantum evolution

Cited by 41 publications

References 61 publications

Revealing memory effects in phase-covariant quantum master equations

Revealing memory effects in phase-covariant quantum master equations

Statistical speed of quantum states: Generalized quantum Fisher information and Schatten speed

Analysis of Lower Bounds for Quantum Control Times and Their Relation to the Quantum Speed Limit

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