Purely quantum memory in closed systems observed via imperfect measurements

Jorge Tabanera-Bravo; Aljaz Godec

doi:10.22331/q-2025-12-11-1938

Purely quantum memory in closed systems observed via imperfect measurements

Jorge Tabanera-Bravo and Aljaz Godec

Mathematical bioPhysics group, Max Planck Institute for Multidisciplinary Sciences, Göttingen 37077, Germany

Published:	2025-12-11, volume 9, page 1938
Editor:	Philip Taranto
Eprint:	arXiv:2506.13689v5
Doi:	https://doi.org/10.22331/q-2025-12-11-1938
Citation:	Quantum 9, 1938 (2025).

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Abstract

The detection and quantification of non-Markovianity, a.k.a. memory, in quantum systems is a central problem in the theory of open quantum systems. There memory is as a result of the interaction between the system and its environment. Little is known, however, about memory effects induced by imperfect measurements on closed systems, where an entanglement with the environment is not possible. We investigate the emergence and characteristics of memory in closed systems observed via imperfect stroboscopic quantum measurements yielding coarse-grained outcomes. We consider ideal and two kinds of imperfect measurements: von Neumann measurements–the analogue of classical lumping–which destroy any coherence in the system, and $\textit{genuinely quantum-lumping}$ Lüders measurements preserving certain quantum correlations. Whereas the conditions for Markov dynamics under von Neumann lumping are the same as for classical dynamics, quantum-lumping requires stronger conditions, i.e. the absence of any detectable coherence. We introduce the concept of $\textit{purely quantum memory}$ having no classical counterpart. We illustrate our results with a quantum walk on a lattice and discuss their implications for dissipative dynamics and decoherence effects induced by more realistic measurements.

Popular summary

Numerous advances in quantum control technologies that we have witnessed in recent decades offer new perspectives and challenges, both fundamentally as well as from the point of view of applications. In this regard, old questions from classical statistical physics are reemerging, now including new concepts such as classicality and quantum memories, which directly interpolate to quantum information theory. In this work, we address the fundamental concept of memory effects but from a different perspective.

The presence of memory gives rise to hard challenges in study the dynamics of physical systems, both classical and quantum. When this memory can be neglected, the physical system is said to be ‘Markovian’. However, memory effects are important when we do not have access to all the degrees of freedom of our system, and we must consider ‘coarse-grained’ evolutions. In this work, we consider a quantum system subjected to consecutive quantum measurements. These quantum measurements are ‘imperfect’ because they do not provide complete information about our quantum system. The reasons for these imperfections can range from classical noise in the measuring apparatus (von Neumann-type measurements) to incomplete collapses of the system's wave function (Luedders-type measurements).

Our results demonstrate that an observed quantum system can display two non-equivalent types of memory. On the one hand, the system can present purely quantum memory in non-collapsed subspaces of Hilbert space, or classical memory that stems from the observer's subjective ignorance.
We illustrate our results using an analytically solvable model of an imperfectly observed a quantum random walker.

► BibTeX data

@article{TabaneraBravo2025purelyquantummemory,
  doi = {10.22331/q-2025-12-11-1938},
  url = {https://doi.org/10.22331/q-2025-12-11-1938},
  title = {Purely quantum memory in closed systems observed via imperfect measurements},
  author = {Tabanera-Bravo, Jorge and Godec, Aljaz},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1938},
  month = dec,
  year = {2025}
}

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[1] Aditya Banerjee, "Quantum scarring enhances non-Markovianity of subsystem dynamics", New Journal of Physics 28 5, 054502 (2026).

[2] Aditya Banerjee, "Quantum scarring enhances non-Markovianity of subsystem dynamics", arXiv:2507.23757, (2025).

[3] Gianluca Teza, Attilio L. Stella, and Trevor GrandPre, "Coarse-Graining via Lumping: Exact Calculations and Fundamental Limitations", arXiv:2512.11974, (2025).

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