Using three-partite GHZ states for partial quantum error-detection in entanglement-based protocols

The problem of noise incidence on qubits taking part of bipartite entanglement-based protocols is addressed. It is shown that the use of a three-partite GHZ state and measurements instead of their EPR counterparts allows the experimenter to detect $2/3$ of the times whenever one of the qubits involved in the measurement is affected by bit-flip noise through the mere observation of unexpected outcomes in the teleportation and superdense coding protocols when compared to the ideal case. It is shown that the use of post-selection after the detection of noise leads to an enhancement in the efficiency of the protocols. The idea is extended to any protocol using entangled states and measurements. Furthermore it is provided a generalization in which GHZ states and measurements with an arbitrary amount of qubits are used instead of EPR pairs, and remarkably, it is concluded that the optimal number of qubits is only three.