Measure how entangled a two-qubit pure state |ψ⟩ = a|00⟩ + b|11⟩ is. Enter the amplitude a (with b = √(1−a²)) to get the entanglement entropy in ebits and the concurrence. A Bell state (a = 0.707) is maximally entangled.
A two-qubit pure state written in Schmidt form is |ψ⟩ = a|00⟩ + b|11⟩ with a² + b² = 1. Its entanglement is quantified by the entanglement entropy — the von Neumann entropy of one qubit's reduced state — S = −p₀log₂p₀ − p₁log₂p₁, where p₀ = a² and p₁ = b². It ranges from 0 (separable) to 1 ebit (maximally entangled).
The concurrence C = 2|a|√(1−a²) is an equivalent measure that runs from 0 to 1. Both peak when a = 1/√2 ≈ 0.707, the balanced superposition of a Bell state, and vanish for a product state where a is 0 or 1.
It is the von Neumann entropy of one qubit after tracing out its partner, measuring how much information the two qubits share. It runs from 0 (no entanglement) to 1 ebit (maximal, a Bell state).
A Bell state such as (|00⟩ + |11⟩)/√2, where a = 1/√2 ≈ 0.707. It has 1 ebit of entanglement entropy and concurrence 1 — measuring one qubit instantly fixes the other.
Concurrence is an entanglement measure for two qubits ranging from 0 to 1. For the pure state a|00⟩ + b|11⟩ it equals 2|a|·|b| = 2|a|√(1−a²).
When the state is separable (a product state), i.e. a = 0 or a = 1. Then one qubit's outcome tells you nothing about the other, and both entropy and concurrence are zero.