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 T^α 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.