Episodic memory does not add up: Verbatim-gist superposition predicts violations of the additive law of probability

Fuzzy-trace theory's assumptions about memory representation are cognitive examples of the familiar superposition property of physical quantum systems. When those assumptions are implemented in a formal quantum model (QEMc), they predict that episodic memory will violate the additive law of probability: If memory is tested for a partition of an item's possible episodic states, the individual probabilities of remembering the item as belonging to each state must sum to more than 1. We detected this phenomenon using two standard designs, item false memory and source false memory. The quantum implementation of fuzzy-trace theory also predicts that violations of the additive law will vary in strength as a function of reliance on gist memory. That prediction, too, was confirmed via a series of manipulations (e.g., semantic relatedness, testing delay) that are thought to increase gist reliance. Surprisingly, an analysis of the underlying structure of violations of the additive law revealed that as a general rule, increases in remembering correct episodic states do not produce commensurate reductions in remembering incorrect states.