Abstract We study the connections between three quantities rembrandt - acquerello stucco that can be used as diagnostics for quantum chaos, i.e., the out-of-time-order correlator (OTOC), Loschmidt echo (LE), and complexity.We generalize the connection between OTOC and LE for infinite dimensions and extend it for higher-order OTOCs and multi-fold LEs.
Novel applications of this intrinsic relation are proposed.We also investigated the relationship between a specific circuit complexity and LE by using the inverted oscillator model and made a conjecture about their hancheng fashion relationship.These relationships signal a deeper connection between these three probes of quantum chaos.