Logical Entropy
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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}iI of f Eigenvalues {ϕi}iI of F
Values {γj}jJ of g Eigenvalues {γj}jJ of G
Partition {f −1(ϕi)}iI Eigenspace DSD of
Partition {g−1(γj)}jJ 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