Quantum scrambling of observable algebras

Paolo Zanardi

doi:10.22331/q-2022-03-11-666

Quantum scrambling of observable algebras

Paolo Zanardi

Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089-0484, USA

Published:	2022-03-11, volume 6, page 666
Eprint:	arXiv:2107.01102v3
Doi:	https://doi.org/10.22331/q-2022-03-11-666
Citation:	Quantum 6, 666 (2022).

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Abstract

In this paper we describe an algebraic/geometrical approach to quantum scrambling. Generalized quantum subsystems are described by an hermitian-closed unital subalgebra $\cal A$ of operators evolving through a unitary channel. Qualitatively, quantum scrambling is defined by how the associated physical degrees of freedom get mixed up with others by the dynamics. Quantitatively, this is accomplished by introducing a measure, the geometric algebra anti-correlator (GAAC), of the self-orthogonalization of the commutant of $\cal A$ induced by the dynamics. This approach extends and unifies averaged bipartite OTOC, operator entanglement, coherence generating power and Loschmidt echo. Each of these concepts is indeed recovered by a special choice of $\cal A$. We compute typical values of GAAC for random unitaries, we prove upper bounds and characterize their saturation. For generic energy spectrum we find explicit expressions for the infinite-time average of the GAAC which encode the relation between $\cal A$ and the full system of Hamiltonian eigenstates. Finally, a notion of ${\cal A}$-chaoticity is suggested.

► BibTeX data

@article{Zanardi2022quantumscramblingof,
  doi = {10.22331/q-2022-03-11-666},
  url = {https://doi.org/10.22331/q-2022-03-11-666},
  title = {Quantum scrambling of observable algebras},
  author = {Zanardi, Paolo},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {666},
  month = mar,
  year = {2022}
}

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