scholarly journals Tight, robust, and feasible quantum speed limits for open dynamics

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 168 ◽  
Author(s):  
Francesco Campaioli ◽  
Felix A. Pollock ◽  
Kavan Modi
Keyword(s):  
Quantum Dynamics ◽  
Quantum Evolution ◽  
Speed Limit ◽  
Mixed States ◽  
Memory Kernel ◽  
Speed Limits ◽  
Open Quantum ◽  
General Quantum ◽  
Almost All

Starting from a geometric perspective, we derive a quantum speed limit for arbitrary open quantum evolution, which could be Markovian or non-Markovian, providing a fundamental bound on the time taken for the most general quantum dynamics. Our methods rely on measuring angles and distances between (mixed) states represented as generalized Bloch vectors. We study the properties of our bound and present its form for closed and open evolution, with the latter in both Lindblad form and in terms of a memory kernel. Our speed limit is provably robust under composition and mixing, features that largely improve the effectiveness of quantum speed limits for open evolution of mixed states. We also demonstrate that our bound is easier to compute and measure than other quantum speed limits for open evolution, and that it is tighter than the previous bounds for almost all open processes. Finally, we discuss the usefulness of quantum speed limits and their impact in current research.

scholarly journals On Time-Local Generators of Quantum Evolution

2014 ◽  
Vol 21 (01n02) ◽  
pp. 1440004 ◽  
Author(s):  
Dariusz Chruściński
Keyword(s):  
Quantum Dynamics ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Master Equations ◽  
Quantum Evolution ◽  
Completely Positive ◽  
Open Quantum ◽  
The Family

We present a basic introduction to the dynamics of open quantum systems based on local-in-time master equations. We characterize the properties of time-local generators giving rise to legitimate completely positive trace preserving quantum evolutions. The analysis of Markovian and non-Markovian quantum dynamics is presented as well. The whole discussion is illustrated by the family of many instructive examples.

scholarly journals Tomographically reconstructed master equations for any open quantum dynamics

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 76 ◽  
Author(s):  
Felix A. Pollock ◽  
Kavan Modi
Keyword(s):  
Quantum Dynamics ◽  
Equation Of Motion ◽  
Memory Kernel ◽  
Reconstruction Procedure ◽  
Quantum Process ◽  
Time Dynamics ◽  
Open Quantum ◽  
Quantum Process Tomography ◽  
Process Tomography ◽  
Long Time

Memory effects in open quantum dynamics are often incorporated in the equation of motion through a superoperator known as the memory kernel, which encodes how past states affect future dynamics. However, the usual prescription for determining the memory kernel requires information about the underlying system-environment dynamics. Here, by deriving the transfer tensor method from first principles, we show how a memory kernel master equation, for any quantum process, can be entirely expressed in terms of a family of completely positive dynamical maps. These can be reconstructed through quantum process tomography on the system alone, either experimentally or numerically, and the resulting equation of motion is equivalent to a generalised Nakajima-Zwanzig equation. For experimental settings, we give a full prescription for the reconstruction procedure, rendering the memory kernel operational. When simulation of an open system is the goal, we show how our procedure yields a considerable advantage for numerically calculating dynamics, even when the system is arbitrarily periodically (or transiently) driven or initially correlated with its environment. Namely, we show that the long time dynamics can be efficiently obtained from a set of reconstructed maps over a much shorter time.

scholarly journals Quantum-speed-limit bounds in an open quantum evolution

2016 ◽  
Vol 94 (5) ◽  
Author(s):  
Nicolás Mirkin ◽  
Fabricio Toscano ◽  
Diego A. Wisniacki
Keyword(s):  
Quantum Evolution ◽  
Speed Limit ◽  
Open Quantum

scholarly journals Entanglement in open quantum dynamics

2009 ◽  
Vol T135 ◽  
pp. 014033 ◽  
Author(s):  
Aurelian Isar
Keyword(s):  
Quantum Dynamics ◽  
Open Quantum

scholarly journals Evaluating the Impacts of Speed Limit Increases on Rural Two-Lane Highways Using Quantile Regression

2021 ◽  
pp. 036119812110197
Author(s):  
Md Shakir Mahmud ◽  
Nischal Gupta ◽  
Babak Safaei ◽  
Hisham Jashami ◽  
Timothy J. Gates ◽  
...  
Keyword(s):  
Quantile Regression ◽  
Spillover Effects ◽  
Speed Limit ◽  
Passenger Cars ◽  
Cross Sectional ◽  
Speed Limits ◽  
Site Specific ◽  
Rural Highways ◽  
Speed Selection ◽  
Numerous Site

Understanding speed selection behavior of drivers following speed limit increases is critically important. To date, the literature has largely focused on freeways and the effects of speed limit changes on two-lane highways remains under researched. Prior research has generally focused on changes to mean speeds, although the speeds of both the highest and lowest drivers are also of great interest. This study investigates trends in free-flow travel speeds following 2017 legislation that increased the posted speed limit from 55 to 65 mph on 943 mi of rural highways in Michigan. Speed data were collected for over 46,000 drivers at 67 increase segments where speed limit increased and 28 control segments where speed limits remained unchanged, before and during each of the two successive years following the speed limit increases. Site-specific traffic, geometric, and cross-sectional information was also collected. Impacts of the speed limit increases on the 15th, 50th, and 85th percentile speeds were evaluated using quantile regression. Separate analyses were conducted for passenger cars and heavy vehicles. Locations where the speed limits were raised experienced increases in travel speeds ranging from 2.8 to 4.8 mph. The control sites experienced marginal changes in speeds, which suggests that any spillover effects of the higher speed limits have been limited. Significant differences were observed across the quantiles with respect to the effects of the speed limit increases, as well as numerous site-specific variables of interest. The results provide important insights about the nature of driver speed selection and the impacts of speed limit increases.

scholarly journals Memory Effects in Quantum Dynamics Modelled by Quantum Renewal Processes

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 905
Author(s):  
Nina Megier ◽  
Manuel Ponzi ◽  
Andrea Smirne ◽  
Bassano Vacchini
Keyword(s):  
Quantum Dynamics ◽  
Open Quantum System ◽  
Open Quantum Systems ◽  
Phenomenological Approach ◽  
Quantum Systems ◽  
Renewal Processes ◽  
Continuous Part ◽  
Trace Distance ◽  
Open Quantum ◽  
And Control

Simple, controllable models play an important role in learning how to manipulate and control quantum resources. We focus here on quantum non-Markovianity and model the evolution of open quantum systems by quantum renewal processes. This class of quantum dynamics provides us with a phenomenological approach to characterise dynamics with a variety of non-Markovian behaviours, here described in terms of the trace distance between two reduced states. By adopting a trajectory picture for the open quantum system evolution, we analyse how non-Markovianity is influenced by the constituents defining the quantum renewal process, namely the time-continuous part of the dynamics, the type of jumps and the waiting time distributions. We focus not only on the mere value of the non-Markovianity measure, but also on how different features of the trace distance evolution are altered, including times and number of revivals.

scholarly journals European birds adjust their flight initiation distance to road speed limits

2013 ◽  
Vol 9 (5) ◽  
pp. 20130417 ◽  
Author(s):  
Pierre Legagneux ◽  
Simon Ducatez
Keyword(s):  
Habitat Structure ◽  
Territory Size ◽  
Speed Limit ◽  
Vehicle Speed ◽  
Flight Initiation Distance ◽  
Speed Limits ◽  
Behavioural Responses ◽  
Road Speed ◽  
Flight Initiation ◽  
Local Speed

Behavioural responses can help species persist in habitats modified by humans. Roads and traffic greatly affect animals' mortality not only through habitat structure modifications but also through direct mortality owing to collisions. Although species are known to differ in their sensitivity to the risk of collision, whether individuals can change their behaviour in response to this is still unknown. Here, we tested whether common European birds changed their flight initiation distances (FIDs) in response to vehicles according to road speed limit (a known factor affecting killing rates on roads) and vehicle speed. We found that FID increased with speed limit, although vehicle speed had no effect. This suggests that birds adjust their flight distance to speed limit, which may reduce collision risks and decrease mortality maximizing the time allocated to foraging behaviours. Mobility and territory size are likely to affect an individuals' ability to respond adaptively to local speed limits.

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