Logical Entropy
Open Access

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
h(π) = 1 − tr[ρ(π)2]
h(π) = sum sq. zeroed h(F:ψ) = sum ab. sq. zeroed