Mutual averaged non-commutativity of quantum operator algebras
arXiv:2312.14019 · doi:10.1063/5.0196994
Abstract
We introduce an elementary measure of non-commutativity between two algebras of quantum operators acting on the same Hilbert space. This quantity, which we call Mutual Averaged Non-commutativity (MAN), is a simple generalization of a type of averaged Out-of-Time-Order-Correlators used in the study of quantum scrambling and chaos. MAN is defined by a Haar averaged squared norm of a commutator and for some types of algebras is manifestly of entropic nature. In particular, when the two algebras coincide the corresponding self-MAN can be fully computed in terms of the structural data of the associated Hilbert space decomposition. Properties and bounds of MAN are established in general and several concrete examples are discussed. Remarkably, for an important class of algebras, -- which includes factors and maximal abelian ones -- MAN can be expressed in the terms of the algebras projections CP-maps. Assuming that the latter can be enacted as physical processes, one can devise operational protocols to directly estimate the MAN of a pair of algebras.
arXiv comment7+5 pages,no figures. Some results added. Version submitted to a Journal
References in corpus (16)
- A bound on chaos
- The Spectrum in the Sachdev-Ye-Kitaev Model
- Lieb-Robinson bounds and the generation of correlations and topological quantum order
- Two-dimensional conformal field theory and the butterfly effect
- Chaos and complexity by design
- Lieb-Robinson and the butterfly effect
- Entanglement of Quantum Evolutions
- On entanglement spreading in chaotic systems
- Information Scrambling over Bipartitions: Equilibration, Entropy Production, and Typicality
- Information Scrambling and Chaos in Open Quantum Systems
- Coherence generating power of quantum unitary maps and beyond
- Quantum Mereology: Factorizing Hilbert Space into Subsystems with Quasi-Classical Dynamics
- Scrambling of Algebras in Open Quantum Systems
- Quantum scrambling of observable algebras
- BROTOCs and Quantum Information Scrambling at Finite Temperature
- Quantum coherence generating power, maximally abelian subalgebras, and Grassmannian Geometry