Isospectral twirling and quantum chaos

Understand

We show that the most important measures of quantum chaos like frame potentials, scrambling, Loschmidt echo, and out-of-time-order correlators (OTOCs) can be described by the unified framework of the isospectral twirling, namely the Haar average of a $k$-fold unitary channel.

• We show that such measures can then be always cast in the form of an expectation value of the isospectral twirling.
• In literature, quantum chaos is investigated sometimes through the spectrum and some other times through the eigenvectors of the Hamiltonian generating the dynamics.
• We show that, by exploiting random matrix theory, these measures of quantum chaos clearly distinguish the finite time profiles of probes to quantum chaos corresponding to chaotic spectra given by the Gaussian Unitary Ensemble (GUE) from the integrable spectra given by Poisson distribution and the Gaussian Diagonal Ensemble (GDE).