We present an elementary proof of the quantum de Finetti representation theorem, a
quantum analog of de Finetti's classical theorem on exchangeable probability assignments.
This contrasts with the original proof of Hudson and Moody [Z. Wahrschein. verw. Geb. 33,
343 (1976)], which relies on advanced mathematics and does not share the same potential
for generalization. The classical de Finetti theorem provides an operational definition of the
concept of an unknown probability in Bayesian probability theory, where probabilities are …