Quantum teleportation and information splitting via four-qubit cluster state and a Bell state

Abstract: Quantum teleportation provides a `bodiless' way of transmitting the quantum state from one object to another, at a distant location, using a classical communication channel and a previously shared entangled state. In this paper, we present a tripartite scheme for probabilistic teleportation of an arbitrary single qubit state, without losing the information of the state being teleported, via a four-qubit cluster state of the form $\left.|{\phi}\right\rangle_{1234}=\left.\alpha|0000\right\rangle+\left.\beta|1010\right\rangle+\left.\gamma|0101\right\rangle-\eta\left.|1111\right\rangle$, as the quantum channel, where the nonzero real numbers $\alpha$, $\beta$, $\gamma$, and $\eta$ satisfy the relation $|\alpha|^2+|\beta|^2+|\gamma|^2+|\eta|^2=1$. With the introduction of an auxiliary qubit with state $\left|0\right\rangle$, using a suitable unitary transformation and a positive-operator valued measure (POVM), the receiver can recreate the state of the original qubit. An important advantage of the teleportation scheme demonstrated here is that, if the teleportation fails, it can be repeated without teleporting copies of the unknown quantum state, if the concerned parties share another pair of entangled qubit. We also present a protocol for quantum information splitting of an arbitrary two-particle system via the aforementioned cluster state and a Bell-state as the quantum channel. Problems related to security attacks were examined for both the cases and it was found that this protocol is secure. This protocol is highly efficient and easy to implement.