Bidirectional Controlled Quantum Teleportation Using Eight-Qubit Quantum Channel in Noisy Environments

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)