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

Gessner, Manuel; Smerzi, Augusto

doi:10.1103/physreva.97.022109

Cited by 46 publications

(46 citation statements)

References 96 publications

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“…Quantum statistical speeds [22][23][24][25][26] offer a possible approach to quantify useful resources in quantum technology tasks. As a major example, the quantum Fisher information 25,27 , which is the quantum statistical speed associated with the Bures distance 25 , was shown to fully characterize metrologically useful entanglement [28][29][30] , that is, the entanglement necessary for sub-shot-noise phase estimation sensitivities 31,32 .…”

Section: Quantifying Computational Advantage Of Grover's Algorithm Wimentioning

confidence: 99%

Quantifying computational advantage of Grover’s algorithm with the trace speed

Gebhart

Pezzé

Smerzi

2021

Sci Rep

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Despite intensive research, the physical origin of the speed-up offered by quantum algorithms remains mysterious. No general physical quantity, like, for instance, entanglement, can be singled out as the essential useful resource. Here we report a close connection between the trace speed and the quantum speed-up in Grover’s search algorithm implemented with pure and pseudo-pure states. For a noiseless algorithm, we find a one-to-one correspondence between the quantum speed-up and the polarization of the pseudo-pure state, which can be connected to a wide class of quantum statistical speeds. For time-dependent partial depolarization and for interrupted Grover searches, the speed-up is specifically bounded by the maximal trace speed that occurs during the algorithm operations. Our results quantify the quantum speed-up with a physical resource that is experimentally measurable and related to multipartite entanglement and quantum coherence.

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Section: Quantifying Computational Advantage Of Grover's Algorithm Wimentioning

confidence: 99%

Quantifying computational advantage of Grover’s algorithm with the trace speed

Gebhart

Pezzé

Smerzi

2021

Sci Rep

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“…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]. Extensive analysis of the current state of knowledge on these topics have been published as reviews in Refs.…”

Section: Extensions and Other Studiesmentioning

confidence: 99%

“…Up to this point we have computed three bounds for the evolution time in this control problem (51), (54) and (55) which are computed without knowledge of the solution to the time-optimal control problem. We also have, from [28], the corresponding QSL time for as a function of θ , T * QSL (θ ) (see Appendix for the explicit expressions) which is computed using such time-optimal solution.…”

Section: Application To a Two-level Systemmentioning

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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“…leading to the a generalized version of the CRB in terms of the β-th absolute central moment [12,14,15]:…”

Section: Generalized Cramér-rao Bounds For Detecting Biased Estimmentioning

confidence: 99%

Diagnosing Imperfections in Quantum Sensors via Generalized Cramér-Rao Bounds

et al. 2020

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Quantum metrology derives its capabilities from the careful employ of quantum resources for carrying out measurements. This advantage however relies on refined data post-processing, assessed based on the variance of the estimated parameter. When Bayesian techniques are adopted, more elements become available for assessing the quality of the estimation. Here we adopt generalized classical Cramér-Rao bounds for looking in detail into a phase estimation experiment performed with quantum light. In particular we show that the third order absolute moment can give a superior capability in revealing biases in the estimation, compared to standard approaches. Our studies point to identify a novel strategy that brings a possible advantage in monitoring the correct operation of high precision sensors.

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

Cited by 46 publications

References 96 publications

Quantifying computational advantage of Grover’s algorithm with the trace speed

Quantifying computational advantage of Grover’s algorithm with the trace speed

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

Diagnosing Imperfections in Quantum Sensors via Generalized Cramér-Rao Bounds

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