Quantum walk-based controlled quantum teleportation schemes under the effect of decoherence in Markovian and non-Markovian regimes

The introduction of quantum walk into quantum teleportation offers a new formation of entanglement between the position space and the coin space using a conditional shift operator. By considering discrete time quantum walks on the cycles, controlled quantum teleportation schemes which can teleport multiple qubits in the multi-dimensional Hilbert spaces are put forward. We also present a decoherence analysis of the proposed protocols in different environments containing dephasing, dissipative and noisy channels using Lindblad operators under the effect of Markovian and non-Markovian regimes.