Existing models of memory incorporate context in only a limited sense, and they fail to accommodate the complementary notion of potentiality. Humans use context in a multitude of ways: (1) to resolve ambiguity between alternative pre-existing meanings, (2) to emphasize particular aspects of something, (3) to identify new and potentially meaningful relationships, and (4) to clarify an idea such that one’s understanding of it goes from ill-defined to well-defined. A powerful model of memory must capture all four. Drawing on elements of vector based information retrieval models, Gärdenfors’ geometric model of conceptual space, and matrix model of memory, we present a quantum approach to memory, and show how it can capture these four senses of contextuality. Though in its infancy, the quantum approach can provide not just exceptionally high-density memory storage but creative capacities as well.