The presence of noise or the interaction with an environment can radically change the dynamics of observables of an otherwise isolated quantum system. We derive a bound on the speed with which observables of open quantum systems evolve. This speed limit is divided into Mandelstam and Tamm’s original time-energy uncertainty relation and a time-information uncertainty relation recently derived for classical systems, and both are generalized to open quantum systems. By isolating the coherent and incoherent contributions to the system dynamics, we derive both lower and upper bounds on the speed of evolution. We prove that the latter provide tighter limits on the speed of observables than previously known quantum speed limits and that a preferred basis of speed operators serves to completely characterize the observables that saturate the speed limits. We use this construction to bound the effect of incoherent dynamics on the evolution of an observable and to find the Hamiltonian that gives the maximum coherent speedup to the evolution of an observable.
García-Pintos, Luis Pedro, Nicholson, Schuyler B., Green, Jason R., del Campo, Adolfo, & Gorshkov, Alexey V. (2022). Unifying Quantum and Classical Speed Limits on Observables. Physical Review. X, 12(1). https://doi.org/10.1103/physrevx.12.011038
García-Pintos, Luis Pedro, Nicholson, Schuyler B., Green, Jason R., et al., "Unifying Quantum and Classical Speed Limits on Observables," Physical Review. X 12, no. 1 (2022), https://doi.org/10.1103/physrevx.12.011038
@article{osti_1846694,
author = {García-Pintos, Luis Pedro and Nicholson, Schuyler B. and Green, Jason R. and del Campo, Adolfo and Gorshkov, Alexey V.},
title = {Unifying Quantum and Classical Speed Limits on Observables},
annote = {The presence of noise or the interaction with an environment can radically change the dynamics of observables of an otherwise isolated quantum system. We derive a bound on the speed with which observables of open quantum systems evolve. This speed limit is divided into Mandelstam and Tamm’s original time-energy uncertainty relation and a time-information uncertainty relation recently derived for classical systems, and both are generalized to open quantum systems. By isolating the coherent and incoherent contributions to the system dynamics, we derive both lower and upper bounds on the speed of evolution. We prove that the latter provide tighter limits on the speed of observables than previously known quantum speed limits and that a preferred basis of speed operators serves to completely characterize the observables that saturate the speed limits. We use this construction to bound the effect of incoherent dynamics on the evolution of an observable and to find the Hamiltonian that gives the maximum coherent speedup to the evolution of an observable.},
doi = {10.1103/physrevx.12.011038},
url = {https://www.osti.gov/biblio/1846694},
journal = {Physical Review. X},
issn = {ISSN 2160-3308},
number = {1},
volume = {12},
place = {United States},
publisher = {American Physical Society (APS)},
year = {2022},
month = {02}}
Univ. of Maryland, College Park, MD (United States); Duke Univ., Durham, NC (United States)
Sponsoring Organization:
National Science Foundation (NSF); US Air Force Office of Scientific Research (AFOSR); John Templeton Foundation; Spanish Ministerio de Ciencia e Innovación; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 222, Issue 594-604https://doi.org/10.1098/rsta.1922.0009
Revue de l'Institut International de Statistique / Review of the International Statistical Institute, Vol. 13, Issue 1/4https://doi.org/10.2307/1400974