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Title: Quantum scrambling of observable algebras
In this paper we describe an algebraic/geometrical approach to quantum scrambling. Generalized quantum subsystems are described by an hermitian-closed unital subalgebra 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 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 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 A and the full system of Hamiltonian eigenstates. Finally, a notion of A -chaoticity is suggested.  more » « less
Award ID(s):
1819189
PAR ID:
10339619
Author(s) / Creator(s):
Date Published:
Journal Name:
Quantum
Volume:
6
ISSN:
2521-327X
Page Range / eLocation ID:
666
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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