Inner products of pure states and their antidistinguishability
Vincent M. Russo, Jamie Sikora · Physical Review A · 2023
We study the antidistinguishability problem, which is a fundamental task in quantum computing. A set of d quantum states is said to be antidistinguishable if there exists a d-outcome positive-operator-valued measure that can perfectly identify which state was not measured. We revisit a conjecture by Havlíçek and Barrett which states that if a set of d pure states has small pairwise inner products, then the set must be antidistinguishable. We develop a certificate of antidistinguishability via semidefinite programming duality and use it to provide a counterexample to this conjecture when d=4. Our work thus opens up again the investigation into which sets of pure states are antidistinguishable.Received 12 September 2022Accepted 6 March 2023DOI:https://doi.org/10.1103/PhysRevA.107.L030202©2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNonlocalityQuantum entanglementQuantum information theoryQuantum Information