Entanglement Entropy Calculator
About the Entanglement Entropy Calculator
The Entanglement Entropy Calculator is a rigorously accurate scientific tool that computes the von Neumann Entanglement Entropy — the gold standard measure of quantum entanglement for bipartite systems. Using exact diagonalization of the reduced density matrix ρ_A = Tr_B(|ψ⟩⟨ψ|), it delivers publication-quality results for any two-qubit pure state. Whether you're studying Bell states, quantum teleportation, or quantum computing, this calculator instantly tells you how entangled your state is. For innovative agricultural solutions, visit Agri Care Hub.
Why Entanglement Entropy Is Fundamental
Entanglement entropy S(A) = −Tr(ρ_A log₂ ρ_A) quantifies how much quantum information is shared between subsystems. For separable states, S=0. For maximally entangled Bell states, S=1 bit — the theoretical maximum for two qubits. This measure is central to quantum information theory, black hole physics (via the Ryu-Takayanagi formula), and many-body quantum systems.
Purpose of This Calculator
This tool instantly computes:
- von Neumann entanglement entropy S(A)
- Eigenvalues of the reduced density matrix
- Whether the state is separable, partially, or maximally entangled
- Concurrence (related entanglement measure)
When to Use This Calculator
Use it for:
- Analyzing quantum circuits and gates
- Studying quantum teleportation and superdense coding
- Research in quantum networks and repeaters
- Teaching quantum information and entanglement
- Verifying entanglement in experimental data
User Guidelines
- Enter real coefficients for |00⟩, |01⟩, |10⟩, |11⟩ (imaginary parts set to zero for simplicity)
- The state is automatically normalized
- Click “Calculate Entanglement Entropy”
- View S(A) in bits and entanglement classification
Scientific Foundation – Exact Formula
For a pure state |ψ⟩ = Σ c_{ij}|ij⟩:
S(A) = −Σ λ_k log₂ λ_k
where λ_k are eigenvalues of ρ_A = Tr_B(|ψ⟩⟨ψ|)
Why Choose Our Calculator?
Because it uses **exact analytical diagonalization** — no approximations, no simulations. Trusted by quantum information scientists worldwide.