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We show how to optimally unambiguously discriminate between two subspaces ofa Hilbert space. In particular we suppose that we are given a quantum system ineither the state \psi_{1}, where \psi_{1} can be any state in the subspaceS_{1}, or \psi_{2}, where \psi_{2} can be any state in the subspace S_{2}, andour task is to determine in which of the subspaces the state of our quantumsystem lies. We do not want to make a mistake, which means that our procedurewill sometimes fail if the subspaces are not orthogonal. This is a special caseof the unambiguous discrimination of mixed states. We present the POVM thatsolves this problem and several applications of this procedure, including thediscrimination of multipartite states without classical communication.Comment: 8 pages, replaced with published versio

Optimal unambiguous discrimination of two subspaces as a case in mixed-state discrimination