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Positive operator-valued measures generalize projective measurements via elements Ei ≥ 0 with ∑i Ei = I.

The Dirac equation (iγμ∂μ − m)ψ = 0 is Lorentz covariant and predicts antiparticle solutions.

Composite quantum systems are described by tensor product Hilbert spaces, and separability corresponds to product states.

The Born rule assigns probability μ(a) = ⟨ψ|Pa|ψ⟩ for outcome a, where Pa is the projection-valued measure associated with the observable.

Quantum channels admit Kraus representations with operators satisfying ∑k Kk†Kk = I.