Controlled quantum teleportation involves a third party as a controller for the teleportation of state. Here, we present the novel protocols for controlling teleportation of the arbitrary two-qubit and three-qubit states through five-qubit and seven-qubit cluster states respectively. In these schemes, Alice sends the arbitrary qubit states to the remote receiver Bob through the cluster states as quantum channels under the control of Charlie. Bob can recover the mentioned states by making appropriate unitary operations, and we point out that the efficiency in our schemes is 100%. In the process of our analysis, we find the classical communication cost in our protocols is remarkably reduced when compared to the previous protocols. We perform the experimental realization of the above protocols on “IBM 16 Melbourne” quantum computer and “IBM quantum simulator” and we calculate the fidelity. We also examine the security analysis against Charlie, and these schemes which we considered here are secure against Charlie’s attacks.

The one-qubit teleportation protocol is one of the most well-known topics of quantum information theory. Indeed, the goal of this quantum protocol is to teleport an arbitrary quantum state. Herein, we investigate the entropic uncertainty relation in the presence of quantum memory (EUR-QM), quantum discord (QD), and fidelity of teleportation under dephasing, dissipative, and noisy environments. We relate the EUR-QM to QD and quantum teleportation and show analytically that there is a fully anti-correlated relation between QD and entropic uncertainty in a dephasing environment. In the process of our analysis, we also find an explicit relationship between the average fidelity of teleportation and the entropic uncertainty of the channel state. Significantly, the results report that the fidelity of teleportation and QD of the channel state are more stable and most efficiently under the influence of a dephasing environment than those under the influence of a dissipative or noisy environment. It turns out that under a dephasing environment, these results can be vital in practical goals where the maximum fidelity of teleportation and minimum uncertainty are required such as in quantum teleportation protocols and quantum computation.

Thermal non-classical correlations quantified by concurrence entanglement, local quantum uncertainty, and quantum coherence in a four-qubit square chain are exactly examined. The influences of the Hamiltonian parameters on the mentioned pairwise quantum criteria and fidelity of teleportation are studied, and the most interesting findings are discussed in detail. It is found that the tuning anisotropy results in enhancing the thermal quantum correlations and coherence as well as average fidelity until achieving maximum values. We persuasively deduce that quantum coherence is a more efficient criterion than that of concurrence and local quantum uncertainty to detect the quantumness of a thermal state.