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Table 5
Ditsets and qudit subspaces without probabilities.
| Classical logical information | Quantum logical information |
|---|---|
 |
Commuting self-adjoint ops. F, G |
| U = {u1, ..., un} | ON basis simultaneous eigenvectors F, G |
| Values {ϕi}i∈I of f | Eigenvalues {ϕi}i∈I of F |
| Values {γj}j∈J of g | Eigenvalues {γj}j∈J of G |
| Partition {f −1(ϕi)}i∈I | Eigenspace DSD of  |
| Partition {g−1(γj)}j∈J | Eigenspace DSD of G |
dits of  ,  |
Qudits of F:  ,  |
dits of  ,  |
Qudits of  :  ,  |
| dit(π) ⊆ U × U | [Qudit(F)] = subspace gen. by qudits of  |
| dit(σ) ⊆ U × U | [Qudit(G)] = subspace gen. by qudits of G |
| dit(π) ∪ dit(σ) ⊆ U × U | [Qudit(F) ∪ Qudit(G)] ⊆ V ⊗ V |
| dit(π) − dit(σ) ⊆ U × U | [Qudit(F) − Qudit(G)] ⊆ V ⊗ V |
| dit(π) ∩ dit(σ) ⊆ U × U | [Qudit(F) ∩ Qudit(G)] ⊆ V ⊗ V |