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Very recently, Lee et al. proposed the first secure quantum teleporationprotocol, where quantum information shared by an arbitrary number of senderscan be transferred to another arbitrary number of receivers. Here, byintroducing quantum walks, a novel secure (n,m) quantum teleportation of sharedquantum secret between n senders and $m$ receivers is presented. Firstly, twokinds of (n,2) teleportation schemes are proposed by n-walker quantum walks onthe line, the first walker of which is driven by three coins, respectively,based on two kinds of coin operators: the homogeneous coins and theposition-dependent coins. Secondly, by increasing the amount of the coins ofthe first walker to m+1, the previous (n,2) scheme can be generalized to (n,m)teleportation scheme. Then, we give the proof of the information security ofour proposed scheme, in which neither any single nor subparties of senders andreceivers can fully access the secret quantum information. Moreover, theprojective measurements are needed, instead of the joint Bell measurements thatare necessary in Lee et al.'s protocol. Our work can also be extended furtherto QWs on the cycle. This work provides an additional relevant instance of therichness of quantum walks for quantum information processing tasks and thusopens the wider application purpose of quantum walks.

Generalized quantum teleportation of shared quantum secret with quantum walks