In a 2000 paper titled "Generalized Schmidt Decomposition and Classification of Three-Quantum-Bit States"[1] Acín et al. described a way of separating out one of the terms of a general tripartite quantum state.
This can be useful in considering measures of entanglement of quantum states.
For a general three-qubit state
|
ψ ⟩ =
a
000
|
0
⟩
|
0
|
+
a
|
there is no way of writing
ψ
λ
λ
but there is a general transformation to
ψ ⟩ =
λ
λ
i ϕ
λ
λ
λ
λ
λ