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 theZandX-basis. Also, in this paper, a new criterion of merit named as (predictability of the controller's qubit (QB) by the eavesdropper) is introduced, and the protocol is improved based on it. Then, the proposed protocol is investigated in two typical noisy channels, the amplitude-damping noise (ADN) and the phase-damping noise (PDN). The analysis of the protocol in the noisy environment shows that it only depends on the amplitude of the initial state and the decoherence noisy rate (DR).