Symmetric bidirectional quantum teleportation using a six-qubit cluster state as a quantum channel

Bidirectional quantum teleportation is a fundamental protocol for exchanging information between two nodes. Till now, all bidirectional protocols have achieved maximum efficiency of $$40\%$$ . Here, we propose new scheme symmetric using six-qubit cluster state as the channel, ( $$3\leftrightarrow 3$$ ) qubit special three-qubit entangled state. The novelty our lies in its generalisation $$N\leftrightarrow N$$ employing 2N-qubit proposed remarkably increased to $$50\%$$ which highest till now. Interestingly, only GHZ-state measurements and four Toffoli-gate operations are necessary independent number (N) qubits be teleported.