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This research investigates how quantum non-Markovianity manifests differently depending on whether the system is described in the Schrödinger or Heisenberg picture, revealing that memory effects relevant to specific information tasks can be inequivalent across these formalisms. The authors establish necessary conditions for detecting such memory effects in one picture and demonstrate that certain witnesses valid in the Schrödinger picture also hold true for the Heisenberg picture. These findings clarify the fundamental requirements for preserving quantum information fidelity in noisy channels, advancing our theoretical understanding of open quantum system dynamics.
Schr\"odinger and Heisenberg non-Markovianity in quantum information tasks
arXiv:2606.30751v2 Announce Type: replace 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 Schr\"odinger 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 Schr\"odinger non-Markovianity in terms of the volume of accessible states does indeed witness non-Markovianity in both pictures at the same time.
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.
arXiv:2606.30751 [quant-ph]
(or arXiv:2606.30751v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2606.30751 Focus to learn more arXiv-issued DOI via DataCite
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