# Quantum speed limits under continuous quantum measurements

## Abstract

The pace of evolution of physical systems is fundamentally constrained by quantum speed limits (QSL), which have found broad applications in quantum science and technology. We consider the speed of evolution for quantum systems undergoing stochastic dynamics due to continuous measurements. It is shown that that there are trajectories for which standard QSL are violated, and we provide estimates for the range of velocities in an ensemble of realizations of continuous measurement records. We determine the dispersion of the speed of evolution and characterize the full statistics of single trajectories. By characterizing the dispersion of the Bures angle, we further show that continuous quantum measurements induce Brownian dynamics in Hilbert space.

- Authors:

- Univ. of Massachusetts, Boston, MA (United States)
- Univ. of Massachusetts, Boston, MA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1525831

- Report Number(s):
- LA-UR-18-22866

Journal ID: ISSN 1367-2630

- Grant/Contract Number:
- 89233218CNA000001

- Resource Type:
- Accepted Manuscript

- Journal Name:
- New Journal of Physics

- Additional Journal Information:
- Journal Volume: 21; Journal Issue: 3; Journal ID: ISSN 1367-2630

- Publisher:
- IOP Publishing

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Atomic and Nuclear Physics; quantum speed limits; continuous quantum measurements; monitored quantum systems

### Citation Formats

```
García-Pintos, Luis Pedro, and del Campo, Adolfo. Quantum speed limits under continuous quantum measurements. United States: N. p., 2019.
Web. doi:10.1088/1367-2630/ab099e.
```

```
García-Pintos, Luis Pedro, & del Campo, Adolfo. Quantum speed limits under continuous quantum measurements. United States. doi:10.1088/1367-2630/ab099e.
```

```
García-Pintos, Luis Pedro, and del Campo, Adolfo. Tue .
"Quantum speed limits under continuous quantum measurements". United States. doi:10.1088/1367-2630/ab099e. https://www.osti.gov/servlets/purl/1525831.
```

```
@article{osti_1525831,
```

title = {Quantum speed limits under continuous quantum measurements},

author = {García-Pintos, Luis Pedro and del Campo, Adolfo},

abstractNote = {The pace of evolution of physical systems is fundamentally constrained by quantum speed limits (QSL), which have found broad applications in quantum science and technology. We consider the speed of evolution for quantum systems undergoing stochastic dynamics due to continuous measurements. It is shown that that there are trajectories for which standard QSL are violated, and we provide estimates for the range of velocities in an ensemble of realizations of continuous measurement records. We determine the dispersion of the speed of evolution and characterize the full statistics of single trajectories. By characterizing the dispersion of the Bures angle, we further show that continuous quantum measurements induce Brownian dynamics in Hilbert space.},

doi = {10.1088/1367-2630/ab099e},

journal = {New Journal of Physics},

number = 3,

volume = 21,

place = {United States},

year = {2019},

month = {3}

}

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