  We introduce a notion of teleportation scheme between subalgebras of
semi-finite von Neumann algebras in the commuting operator model of locality.
Using techniques from subfactor theory, we present unbiased teleportation
schemes for relative commutants $N'\cap M$ of a large class of finite-index
inclusions $N\subseteq M$ of tracial von Neumann algebras, where the unbiased
condition means that no information about the teleported observables are
contained in the classical communication sent between the parties. For a large
class of subalgebras $N$ of matrix algebras $M_n(\mathbb{C})$, including those
relevant to hybrid classical/quantum codes, we show that any tight
teleportation scheme for $N$ necessarily arises from an orthonormal unitary
Pimsner-Popa basis of $M_n(\mathbb{C})$ over $N'$, generalising work of Werner.
Combining our techniques with those of Brannan-Ganesan-Harris, we compute
quantum chromatic numbers for a variety of quantum graphs arising from
finite-dimensional inclusions $N\subseteq M$.
