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Table 6
Probabilities applied to ditsets and qudit spaces.
| “Classical” Logical Entropy | Quantum Logical Entropy |
|---|---|
| Pure state density matrix, e.g., ρ(0U) | Pure state density matrix ρ(ψ) |
| U = {u1, …, un} | ON basis simultaneous eigenvectors F, G |
| p × p on U × U | ρ(ψ)⊗ρ(ψ) on V ⊗ V |
| h(0U) = 1 − tr[ρ(0U)2] = 0 | h(ρ(ψ)) = 1 − tr[ρ(ψ)2] = 0 |
| h(π) = p × p(dit(π)) | h(F:ψ) = tr[P[qudit(F)] ρ(ψ) ⊗ ρ(ψ)] |
| h(π, σ) = p × p(dit(π) ∪ dit(σ)) | h(F,G:ψ) = tr[P[qudit(F) ∪ qudit(G)] ρ(ψ)⊗ρ(ψ)] |
| h(π|σ) = p × p(dit(π) − dit(σ)) | h(F|G:ψ) = tr[P[qudit(F) − qudit(G)] ρ(ψ) ⊗ ρ(ψ)] |
| m(π, σ) = p × p(dit(π) ∩ dit(σ)) | m(F,G:ψ) = tr[P[qudit(F) ∩ qudit(G)] ρ(ψ) ⊗ ρ(ψ)] |
| h(π) = h(π|σ) + m(π,σ) | h(F:ψ) = h(F|G:ψ) + m(F,G:ψ) |
| h(π) = 2-draw prob. diff. f-values | h(F:ψ) = 2-meas. prob. diff. F-eigenvalues |
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| h(π) = 1 − tr[ρ(π)2] |
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h(π) = sum sq. zeroed  |
h(F:ψ) = sum ab. sq. zeroed  |