Quantum Teleportation in the Commuting Operator Framework

We introduce a notion of teleportation scheme between subalgebras semi-finite von Neumann algebras in the commuting operator model locality. Using techniques from subfactor theory, we present unbiased schemes for relative commutants $$N'\cap M$$ large class finite-index inclusions $$N\subseteq tracial algebras, where condition means that no information about teleported observables is contained classical communication sent parties. For N matrix $$M_n({\mathbb {C}})$$ , including those relevant to hybrid classical/quantum codes, show any tight necessarily arises an orthonormal unitary Pimsner–Popa basis over $$N'$$ generalising work Werner (J Phys A 34(35):7081–7094, 2001). Combining our with Brannan–Ganesan–Harris Math 63(11): 112204, 2022) compute quantum chromatic numbers variety graphs arising finite-dimensional .