  In this work, a novel protocol is proposed for bidirectional controlled
quantum teleportation (BCQT) in which a quantum channel is used with the
eight-qubit entangled state. Using the protocol, two users can teleport an
arbitrary entangled state and a pure two-qubit state (QBS) to each other
simultaneously under the permission of a third party in the role of controller.
This protocol is based on the controlled-not operation, appropriate
single-qubit (SIQ) UOs and SIQ measurements in the Z and X-basis. Reduction of
the predictability of the controller's qubit (QB) by the eavesdropper and also,
an increasing degree of freedom of controller for controlling one of the users
or both are other features of this protocol. Then, the proposed protocol is
investigated in two typical noisy channels include the amplitude-damping noise
(ADN) and the phase-damping noise (PDN). And finally, analysis of the protocol
shows that it only depends on the amplitude of the initial state and the
decoherence noisy rate (DR).
