Quantum state exclusion with many copies

Abstract: Quantum state exclusion is the task of identifying at least one state from a known set that was not used in the preparation of a quantum system. In particular, a given set of quantum states is said to admit state exclusion if there exists a measurement such that, for each state in the set, some measurement outcome rules it out with certainty. However, state exclusion is not always possible in the single-copy setting. In this paper, we investigate whether access to multiple identical copies enables state exclusion. We prove that for any set of three or more pure states, state exclusion becomes possible with a finite number of copies. We further show that the required number of copies may be arbitrarily large -- in particular, for every natural number $N$, we construct sets of states for which exclusion remains impossible with $N$ or fewer copies.