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

Francesco Campaioli; Felix A. Pollock; Kavan Modi

doi:10.22331/q-2019-08-05-168

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

Francesco Campaioli, Felix A. Pollock, and Kavan Modi

School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia

Published:	2019-08-05, volume 3, page 168
Eprint:	arXiv:1806.08742v5
Doi:	https://doi.org/10.22331/q-2019-08-05-168
Citation:	Quantum 3, 168 (2019).

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Abstract

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.

Featured image: The euclidean distance $D(\rho,\sigma)=\lVert r - s\rVert_2$ between the generalised Bloch vectors $r$ and $s$, associated with states $\rho$ and $\sigma$, induces a tight bound $T_D$ on the minimal time of evolution $\tau$ between them, for arbitrary open dynamics. This bound is robust under composition, as well as under mixing with the fixed state of the considered dynamics, thus invariant under pure depolarisation for unitary and unital dynamics.

► BibTeX data

@article{Campaioli2019tightrobust,
  doi = {10.22331/q-2019-08-05-168},
  url = {https://doi.org/10.22331/q-2019-08-05-168},
  title = {Tight, robust, and feasible quantum speed limits for open dynamics},
  author = {Campaioli, Francesco and Pollock, Felix A. and Modi, Kavan},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {3},
  pages = {168},
  month = aug,
  year = {2019}
}

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