Operational Quantum Mereology and Minimal Scrambling

Paolo Zanardi; Emanuel Dallas; Faidon Andreadakis; Seth Lloyd

doi:10.22331/q-2024-07-11-1406

Operational Quantum Mereology and Minimal Scrambling

Paolo Zanardi^1,2, Emanuel Dallas¹, Faidon Andreadakis¹, and Seth Lloyd^3,4

¹Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089-0484, USA
²Department of Mathematics, University of Southern California, Los Angeles, California 90089-2532, USA
³MIT Department of Mechanical Engineering, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
⁴Turing Inc., Cambridge, MA 02139, USA

Published:	2024-07-11, volume 8, page 1406
Eprint:	arXiv:2212.14340v5
Doi:	https://doi.org/10.22331/q-2024-07-11-1406
Citation:	Quantum 8, 1406 (2024).

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Abstract

In this paper we will attempt to answer the following question: what are the natural quantum subsystems which emerge out of a system's dynamical laws? To answer this question we first define generalized tensor product structures (gTPS) in terms of observables, as dual pairs of an operator subalgebra $\cal A$ and its commutant. Second, we propose an operational criterion of minimal information scrambling at short time scales to dynamically select gTPS. In this way the emergent subsystems are those which maintain the longest informational identity. This strategy is made quantitative by defining a Gaussian scrambling rate in terms of the short-time expansion of an algebraic version of the Out of Time Order Correlation (OTOC) function i.e., the $\cal A$-OTOC. The Gaussian scrambling rate is computed analytically for physically important cases of general division into subsystems, and is shown to have an intuitive and compelling physical interpretation in terms of minimizing the interaction strength between subsystems.

► BibTeX data

@article{Zanardi2024operationalquantum,
  doi = {10.22331/q-2024-07-11-1406},
  url = {https://doi.org/10.22331/q-2024-07-11-1406},
  title = {Operational {Q}uantum {M}ereology and {M}inimal {S}crambling},
  author = {Zanardi, Paolo and Dallas, Emanuel and Andreadakis, Faidon and Lloyd, Seth},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1406},
  month = jul,
  year = {2024}
}

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[2] Faidon Andreadakis and Paolo Zanardi, "Tensor Product Structure Geometry under Unitary Channels", Quantum 9, 1668 (2025).

[3] Paolo Zanardi, Emanuel Dallas, and Faidon Andreadakis, "Mereological quantum phase transitions", Physical Review A 113 4, 042201 (2026).

[4] Nicolas Loizeau and Dries Sels, "Quantum Mereology and Subsystems from the Spectrum", Foundations of Physics 55 1, 3 (2025).

[5] Antoine Soulas, "Disentangling tensor product structures", International Journal of Quantum Information 23 07, 2550027 (2025).

[6] Arsalan Adil, Manuel S. Rudolph, Andrew Arrasmith, Zoë Holmes, Andreas Albrecht, and Andrew Sornborger, "Search for classical subsystems in quantum worlds", Physical Review D 113 10, 103535 (2026).

[7] Faidon Andreadakis, Emanuel Dallas, and Paolo Zanardi, "Operator space entangling power of quantum dynamics and local operator entanglement growth in dual-unitary circuits", Physical Review A 110 5, 052416 (2024).

[8] Antonio F. Rotundo, Paolo Perinotti, and Alessandro Bisio, "Effective dynamics from minimizing dissipation", Physical Review Research 7 4, 043019 (2025).

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[11] Faidon Andreadakis, Emanuel Dallas, and Paolo Zanardi, "Long-time quantum scrambling and generalized tensor product structures", Physical Review A 109 5, 052424 (2024).

[12] Paolo Zanardi, "Mutual averaged non-commutativity of quantum operator algebras", Journal of Mathematical Physics 65 6, 062202 (2024).

[13] Augustin Vanrietvelde, Octave Mestoudjian, and Pablo Arrighi, "Partitions in quantum theory", arXiv:2506.22218, (2025).

[14] Ovidiu Cristinel Stoica, "Structural Realism and the underdetermination of the physical meaning", Journal of Physics Conference Series 2948 1, 012014 (2025).

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