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def definition def or abbrev

entanglementEntropy

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formal statement (Lean)

 105noncomputable def entanglementEntropy (sys : BipartiteSystem) (eigenvalues : Fin sys.dim_A → ℝ)
 106    (normalized : (Finset.univ.sum eigenvalues) = 1)
 107    (nonneg : ∀ i, eigenvalues i ≥ 0) : ℝ :=

proof body

Definition body.

 108  -Finset.univ.sum fun i =>
 109    if h : eigenvalues i > 0 then
 110      eigenvalues i * Real.log (eigenvalues i)
 111    else 0
 112
 113/-- **THEOREM**: Entanglement entropy is non-negative. -/

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