A Finite de Finetti Theorem for Infinite-Dimensional Systems

D'Cruz, Christian; Osborne, Tobias J.; Schack, Ruediger

A Finite de Finetti Theorem for Infinite-Dimensional Systems

Authors

D'Cruz, Christian

Osborne, Tobias J.

Schack, Ruediger

Description

We formulate and prove a de Finetti representation theorem for finitely exchangeable states of a quantum system consisting of k infinite-dimensional subsystems. The theorem is valid for states that can be written as the partial trace of a pure state chosen from a family of subsets C_n of the full symmetric subspace for $n$ subsystems. We show that such states become arbitrarily close to mixtures of pure power states as n increases. We give a second equivalent characterization of the family C_n.
4 pages, 2 figures