Quantum information spreading via higher-order operator correlators

Mehmet Süzen introduces N-Operator Correlators (NOC), a direct generalization of Out-of-Time-Ordered Correlators (OTOCs) that uses N operators instead of the conventional two to quantify quantum information spreading. Drawing on the concept of N-point correlation functions from cosmology, NOC formalizes higher-order operator correlators and argues that sampling a larger set of probe operators reduces the bias and restricted perspective inherent in two-operator OTOC diagnostics. The construction retains the out-of-time ordering structure but allows thermal averaging at finite temperature, enabling a more flexible probe of operator growth and scrambling across different measurement bases.

The study demonstrates NOC computations analytically in two solvable models: a single qubit in a longitudinal field and an XYZ two-qubit system. For each model the author computes time-evolved operator thermal averages, exhibits explicit NOC expressions, and contrasts their behavior with conventional two-operator OTOCs, showing how additional operators capture features of information spreading that pairwise correlators miss. The presentation is concise and pedagogical, offering closed-form examples and equations that serve as a practical introduction to applying generalized operator correlators in quantum mechanics.