Violation of Diagonal Non-Invasiveness: A Hallmark of Non-Classical Memory Effects

An operational (measurement based) scheme that connects measurement invasiveness and the presence of non-classical memory effects in open quantum systems is defined. Its underlying theoretical basis relies on a non-invasive measurability of (memoryless) quantum Markovian dynamics when the corresponding observable is diagonal in the same basis as the system density matrix. In contrast, violation of this property can be related to intrinsic non-classical memory effects. Related conditions for violation of Leggett-Garg inequality due to quantum memory effects emerge from this perspective. The developed approach applies to open quantum dynamics whose time-evolution is derived from a full unitary (microscopic) description, stochastic Hamiltonian dynamics, as well as for a broad class of non-unitary system-environment models (bipartite Lindblad equations).