Entanglement Entropy

S = −Tr(ρ_A log ρ_A) — Bipartite Quantum Systems

For a bipartite quantum system |ψ⟩ ∈ H_A ⊗ H_B, the entanglement entropy S(A) = −Tr(ρ_A log ρ_A) where ρ_A = Tr_B|ψ⟩⟨ψ| is the reduced density matrix. The Schmidt decomposition |ψ⟩ = Σλ_i|i_A⟩|i_B⟩ reveals the entanglement structure. Maximum entropy = log(min(dim H_A, dim H_B)).

System dimension d

Entanglement parameter α

α = 0.50

State mixing β

β = 0.30

S(A) entropy:—

S_max = log(d):—

Normalized S/S_max:—

Schmidt rank:—

Purity Tr(ρ²):—

Schmidt eigenvalues λᵢ

Reduced density matrix ρ_A