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arXiv:2012.03029

Generalized quantum teleportation of shared quantum secret with quantum walks

Hengji Li, Jian Li, Xiu‐Bo Chen

Published Dec 5, 2020• 0 citations
arXivHTMLPDF

Abstract

Very recently, Lee et al. proposed the first secure quantum teleporation protocol, where quantum information shared by an arbitrary number of senders can be transferred to another arbitrary number of receivers. Here, by introducing quantum walks, a novel secure (n,m) quantum teleportation of shared quantum secret between n senders and $m$ receivers is presented. Firstly, two kinds of (n,2) teleportation schemes are proposed by n-walker quantum walks on the line, the first walker of which is driven by three coins, respectively, based on two kinds of coin operators: the homogeneous coins and the position-dependent coins. Secondly, by increasing the amount of the coins of the 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 of our proposed scheme, in which neither any single nor subparties of senders and receivers can fully access the secret quantum information. Moreover, the projective measurements are needed, instead of the joint Bell measurements that are necessary in Lee et al.'s protocol. Our work can also be extended further to QWs on the cycle. This work provides an additional relevant instance of the richness of quantum walks for quantum information processing tasks and thus opens the wider application purpose of quantum walks.

DOI
10.48550/arxiv.2012.03029

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We introduce some new perfect state transfer and teleportation schemes by quantum walks with two coins. Encoding the transferred information in coin 1 state and alternatively using two coin operators, we can perfectly recover the information on coin 1 state at target position only by at most two times of flipping operation. Based on quantum walks with two coins either on the line or on the NNN-circle, we can perfectly transfer any qubit state. In addition, using quantum walks with two coins either on complete graphs or regular graphs, we can first implement perfect qudit state transfer by quantum walks. Compared with existing schemes driven by one coin, more general graph structures can be used to perfectly transfer more general state. Moreover, the external control of coin operator during the transmitting process can be decreased greatly. Selecting coin 1 as the sender and coin 2 as the receiver, we also study how to realize generalized teleportation over long steps of walks by the above quantum walk models. Because quantum walks is an universal quantum computation model, our schemes may provide an universal platform for the design of quantum network and quantum computer.
Quantum teleportation is a fundamental building block of quantum communications and quantum computations, transferring quantum states between distant physical entities. In the context of quantum secret sharing, the teleportation of quantum information shared by multiple parties without concentrating the information at any place is essential, and this cannot be realized by any previous scheme. We propose and experimentally demonstrate a novel teleportation protocol that enables one to perform this task. It is jointly performed by distributed participants, while none of them can fully access the information. Our scheme can be extended to arbitrary numbers of senders and receivers and to fault-tolerant quantum networks by incorporating error-correction codes.
Based on the teleportation by quantum walk, a quantum secret sharing scheme with credible authentication is proposed.Using the Hash function and quantum local operation, combined with the two-step quantum walks circuit on the line, the identity authentication and the teleportation of the secret information in distribution phase are realized.Participants collaborate honestly to recover secret information based on particle measurement results, preventing untrusted agents and external attacks from obtaining useful information.Due to the application of quantum walk, the sender does not need to prepare the necessary entangled state in advance, simply encodes the information to be sent in the coin state, and applies the conditional shift operator between the coin space and the position space to produce the entangled state necessary for quantum teleportation.Security analysis shows that the protocol can effectively resist intercept/resend attacks, entanglement attacks, participant attacks, and impersonation attacks.In addition, the quantum walk circuit used has been implemented in many different physical systems and experiments, so this quantum secret sharing scheme may be achievable in the future.
Very recently, Lee et al. proposed a secure quantum teleportation protocol to transfer shared quantum secret between multiple parties in a network [Phys. Rev. Lett. 124 060501 (2020)]. This quantum network is encoded with a maximally entangled GHZ state. In this paper, we consider a partially entangled GHZ state as the entanglement channel, where it can achieve, probabilistically, unity fidelity transfer of the state. Two kinds of strategies are given. One arises when an auxiliary particle is introduced and a general evolution at any receiver’s location is then adopted. The other one involves performing a single generalized Bell-state measurement at the location of any sender. This could allow the receivers to recover the transmitted state with a certain probability, in which only the local Pauli operators are performed, instead of introducing an auxiliary particle. In addition, the successful probability is provided, which is determined by the degree of entanglement of the partially multipartite entangled state. Moreover, the proposed protocol is robust against the bit and phase flip noise.
We introduce some new perfect state transfer and generalized long-distance teleportation schemes by quantum walks with two coins. By encoding the transferred information in the coin-1 state and alternately using two coin operators, we can perfectly recover the information in the coin-1 state at the target position by at most two flipping operations. On the basis of quantum walks with two coins on either a line or an N -circle, we can perfectly transfer any qubit state. In addition, using quantum walks with two coins on regular graphs, we can first implement a perfect qudit state transfer by quantum walks. Compared with existing schemes driven by one coin, more general graph structures can be used to perfectly transfer a more general state. We also study how to realize generalized teleportation over long-distance walks by the above quantum walk models.
Recently, Wang et al. [Wang et al., Quantum Inf. Process. 16 (2017) 221] developed generalized teleportation schemes based on different quantum walks structures. In their paper, an interesting open question is whether there are other graphs suitable for teleportation. Here, we extend the results of quantum teleportation of an unknown qubit state by means of discrete-time quantum walks and propose two kinds of schemes for quantum teleportation by means of discrete-time quantum walks on N-lines and N-cycles, respectively. Likewise, prior quantum entanglement is unnecessary for teleportation and quantum entanglement is generated by means of quantum walks. This further opens wider applications of quantum walks in quantum communication protocols.