Quantum scrambling of observable algebras
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.
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Cited by
[1] Faidon Andreadakis, Namit Anand, and Paolo Zanardi, "Scrambling of algebras in open quantum systems", Physical Review A 107 4, 042217 (2023).
[2] Faidon Andreadakis and Paolo Zanardi, "Coherence generation, symmetry algebras and Hilbert space fragmentation", arXiv:2212.14408, (2022).
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