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[[Quantum superposition]] states that any physical system simultaneously exists in all of its possible [[quantum state|states]], the number of which is exponential in the number of entities composing the system. The strength of presence of each possible state in the superposition{{snd}} i.e., the probability with which it would be observed if measured{{snd}} is represented by its [[probability amplitude]] coefficient. The assumption that these coefficients must be represented physically disjointly from each other, i.e., locally, is nearly universal in the [[quantum mechanics|quantum theory]]/[[quantum computing]] literature.
Specifically, If we consider an SDR model in which the overall population consists of Q clusters, each having K binary units, so that each coefficient is represented by a set of Q units, one per cluster. We can then consider the particular world state, X, whose coefficient's representation, R(X), is the set of Q units active at time t to have the maximal probability and the probabilities of all other states, Y, to correspond to the size of the intersection of R(Y) and R(X). Thus, R(X) simultaneously serves both as the representation of the particular state, X, and as a probability distribution over all states. When any given code, e.g., R(A), is active, all other codes stored in the model are also physically active in proportion to their intersection with R(A). Thus, SDR provides a classical realization of quantum superposition in which probability amplitudes are represented directly and implicitly by sizes of [[set intersection]]s. If algorithms exist for which the time it takes to store (learn) new representations and to find the closest-matching stored representation ([[Bayesian inference|probabilistic inference]]) remains constant as additional representations are stored, this would meet the criterion of [[quantum computing]].
==Applications==
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