Fourth-order ordering-sensitive Bargmann invariants supply the first universal pairwise criterion for set coherence, and applying it to all pairs yields a complete test for any finite family of states.
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Visibility inequalities in n-path interferometers are violated by pure qubit states up to a derived bound, witnessing preparation contextuality via overlap relations.
Two quantum states ρ₁ and ρ₂ commute exactly when tr(ρ₁²ρ₂²) = tr(ρ₁ ρ₂ ρ₁ ρ₂).
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A low order Bargmann invariant hierarchy for set coherence
Fourth-order ordering-sensitive Bargmann invariants supply the first universal pairwise criterion for set coherence, and applying it to all pairs yields a complete test for any finite family of states.
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Interference visibility as a witness of preparation contextuality via overlap inequalities
Visibility inequalities in n-path interferometers are violated by pure qubit states up to a derived bound, witnessing preparation contextuality via overlap relations.
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Commutativity from a single Bargmann invariant equality
Two quantum states ρ₁ and ρ₂ commute exactly when tr(ρ₁²ρ₂²) = tr(ρ₁ ρ₂ ρ₁ ρ₂).