Schrödinger and Heisenberg non-Markovianity in quantum information tasks
Abstract
Quantum non-Markovianity has been widely studied and connected to the existence of memory effects in the dynamics of open systems. Surprisingly, working in the Schrödinger or in the Heisenberg picture can provide inequivalent description non-Markovianity: a process can appear to be memoryless in one picture, while displaying memory effects in the other. Here, we investigate which kind of memory is relevant for different quantum information tasks. Some of them, such as sending information via a noisy channel, require memory in both pictures in order to exhibit revivals in the task performance. For others, only one type of memory is sufficient. We also provide necessary conditions for non-Markovianity in both pictures by only considering the dynamics in one picture, showing for instance that the previously considered witness of Schrödinger non-Markovianity in terms of the volume of accessible states does indeed witness non-Markovianity in both pictures at the same time.
Related
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BibTeX
@misc{settimo2026schrödinger,
title = {{Schrödinger and Heisenberg non-Markovianity in quantum information tasks}},
author = {Federico Settimo and Kimmo Luoma and Jyrki Piilo and Bassano Vacchini and Dariusz Chruściński and Andrea Smirne},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.30751},
eprint = {2606.30751},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.30751},
}
RIS
TY - UNPB
TI - Schrödinger and Heisenberg non-Markovianity in quantum information tasks
AU - Federico Settimo
AU - Kimmo Luoma
AU - Jyrki Piilo
AU - Bassano Vacchini
AU - Dariusz Chruściński
AU - Andrea Smirne
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2606.30751
UR - https://arxiv.org/abs/2606.30751
AB - Quantum non-Markovianity has been widely studied and connected to the existence of memory effects in the dynamics of open systems. Surprisingly, working in the Schrödinger or in the Heisenberg picture can provide inequivalent description non-Markovianity: a process can appear to be memoryless in one picture, while displaying memory effects in the other. Here, we investigate which kind of memory is relevant for different quantum information tasks. Some of them, such as sending information via a noisy channel, require memory in both pictures in order to exhibit revivals in the task performance. For others, only one type of memory is sufficient. We also provide necessary conditions for non-Markovianity in both pictures by only considering the dynamics in one picture, showing for instance that the previously considered witness of Schrödinger non-Markovianity in terms of the volume of accessible states does indeed witness non-Markovianity in both pictures at the same time.
ER -