Efficient methods for choosing quantum channel in teleportation and bidirectional teleportation

The tensor representation of quantum teleportation shows the internal connection between Bell basis measurement matrix Tα and channel parameter matrix (CPM) R. An explicit CPM criterion based on the tensor representation is derived. This criterion can be used to judge whether a quantum state can be employed as the quantum channel or not in teleportation and bidirectional teleportation, and it provides us more flexible choices to construct the quantum channel.