An operational definition of quantum information scrambling

Abstract: Quantum information scrambling (QIS) is a characteristic feature of several quantum systems, ranging from black holes to quantum communication networks. While accurately quantifying QIS is crucial to understanding many such phenomena, common approaches based on the tripartite information have limitations due to the accessibility issues of quantum mutual information, and do not always properly take into consideration the dependence on the encoding input basis. To address these issues, we propose a novel and computationally efficient QIS quantifier, based on a formulation of QIS in terms of quantum state discrimination. We show that the optimal guessing probability, which reflects the degree of QIS induced by an isometric quantum evolution, is directly connected to the accessible min-information, a generalized channel capacity based on conditional min-entropy, which can be cast as a convex program and thus computed efficiently. By applying our proposal to a range of examples with increasing complexity, we illustrate its ability to capture the multifaceted nature of QIS in all its intricacy.