Quantum scrambling of observable algebras

In this paper we describe an algebraic/geometrical approach to quantum scrambling. Generalized subsystems are described by hermitian-closed unital subalgebra A of operators evolving through a unitary channel. Qualitatively, scrambling is defined how the associated physical degrees freedom get mixed up with others dynamics. Quantitatively, accomplished introducing measure, geometric algebra anti-correlator (GAAC), self-orthogonalization commutant induced This extends and unifies averaged bipartite OTOC, operator entanglement, coherence generating power Loschmidt echo. Each these concepts indeed recovered special choice mathvariant="script">A. We compute typical values GAAC for random unitaries, prove upper bounds characterize their saturation. For generic energy spectrum find explicit expressions infinite-time average which encode relation between full system Hamiltonian eigenstates. Finally, notion xmlns:mml="http://www.w3.org/1998/Math/MathML">A-chaoticity suggested.