UDP–UDA equivalence for arbitrary Pauli measurement schemes

Determine whether uniquely determining every pure state among pure states (UDP) implies uniquely determining every pure state among all states, including mixed states (UDA), for every Pauli measurement scheme.

Background

The paper establishes that four-set-free omitted Pauli supports guarantee universal UDA for systems with at least three qubits, and that universal UDP and UDA are equivalent for pairwise-commuting omitted supports. These results leave open the possibility of a separation between UDP and UDA only for noncommuting omitted supports containing a commuting zero-sum four-set.

A solution would determine whether retained Pauli expectation values can exclude every competing pure state while still admitting a mixed-state explanation. The paper further notes that the answer depends on the interaction between the four-set and the other omitted observables.