Quantum state exclusion with many copies

TL;DR

This paper investigates whether multiple copies of a quantum system enable the exclusion of certain states, proving that for three or more pure states, state exclusion becomes possible with enough copies, but some sets require arbitrarily many.

Contribution

The authors demonstrate that multiple copies can enable quantum state exclusion for sets of three or more pure states, and they construct examples requiring arbitrarily many copies.

Findings

State exclusion is impossible with a single copy for certain sets.

Multiple copies can enable state exclusion for any set of three or more pure states.

Some sets of states require arbitrarily many copies for exclusion.

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. A set of quantum states is said to admit state exclusion if there exists a measurement whose outcomes can be put in one-to-one correspondence with the states in the set, such that each outcome rules out its corresponding state with certainty (while possibly also ruling out other states), and each outcome occurs with nonzero probability for at least one state in the set. State exclusion, however, is not always possible in the single-copy setting. In this paper, we investigate whether access to multiple identical copies of the system 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. Moreover, we show that the number of copies required may be arbitrarily large: in particular, for every natural number $N$, we construct sets of states for which state exclusion remains impossible with $N$ or fewer copies.