recognition /
Quantum /
Quantum.EntanglementEntropy /
explainer
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formal statement (Lean)
105 noncomputable 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. -/
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (9)
Lean names referenced from this declaration's body.
entropy
in IndisputableMonolith.Foundation.InitialCondition
decl_use
is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
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is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
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is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
normalized
in IndisputableMonolith.NavierStokes.RunningMaxNormalization
decl_use
BipartiteSystem
in IndisputableMonolith.Quantum.EntanglementEntropy
decl_use
entropy
in IndisputableMonolith.Thermodynamics.BoltzmannDistribution
decl_use
entropy
in IndisputableMonolith.Thermodynamics.PartitionFunction
decl_use