Non-adaptive equivalence tests now require Ω(1/ε²) samples, even with just two quantum states, whereas state certification achieves comparable results without needing adaptive algorithms. This contrasts sharply with prior work demonstrating no asymptotic benefit of adaptivity when using trace distance as the decision gap. These new findings reveal clear separations in sample complexity between verifying if states are identical, independent or simply close to a target specification, all measured via fidelity.
Singapore Team Bounds State Certification Sample Needs with Rank R
Non-adaptive equivalence tests now require Ω(1/ε²) samples, even with just two quantum states, whereas state certification achieves comparable results without needing adaptive algorithms. This contrasts sharply with prior work demonstrating no asymptotic benefit of adaptivity when using trace distance as the decision gap. These new findings reveal clear separations in sample complexity between verifying if states are identical, independent or simply close to a target specification, all measur...