# Entropy of entanglement

The **entropy of entanglement** is an entanglement measure for a bipartite pure states. It is defined as the von Neumann entropy of one of the reduced states. That is, for a pure state *ρ**A**B* = ∣Ψ⟩⟨Ψ∣*A**B*, it is given by:

E(*ρ*) ≡ S(*ρ**A*) = S(*ρ**B*),

where *ρ**A* = Tr*B*(∣Ψ⟩⟨Ψ∣) and *ρ**B* = Tr*A*(∣Ψ⟩⟨Ψ∣).

Many entanglement measures reduce to the entropy of entanglement when evaluated on pure states. Among those are

- Distillable entanglement
- Entanglement cost
- Entanglement of formation
- Relative entropy of entanglement
- Squashed entanglement

Some entanglement measures that do not reduce to the entropy of entanglement are

### See also

Category:Entropy Category:Handbook of Quantum Information Category:Entanglement

Last modified:

Monday, October 26, 2015 - 17:56