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arXiv:1802.02400

Quantum communication protocols by quantum walks with two coins

Yun Shang, Wang, Yu, Li, Meng, Ruqian Lu

Published Feb 7, 2018• 3 citations
arXivHTMLPDF

Abstract

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 $N$-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.

DOI
10.48550/arxiv.1802.02400

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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.
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.
Abstract Perfect state transfer has attracted a great deal of attention recently due to its crucial role in quantum communication and scalable quantum computation. In this paper, we propose the perfect state transfer algorithms with a pair of sender-receiver and two pairs of sender-receiver on the complete bipartite graph respectively. The algorithm with a pair of sender-receiver is implemented through discrete-time quantum walk, flexibly setting the coin operators based on the positions of the sender and receiver. The algorithm with two pairs of sender-receiver ensures that the two quantum states are distributed on both sides of the complete bipartite graph during the process, thereby achieving perfect state transfer. In addition, the quantum circuits corresponding to the algorithms are provided. The algorithms can transfer an arbitrary quantum state and can simultaneously transfer two arbitrary quantum states from the senders to the receivers in any case. Moreover, the algorithms are not only applicable to complete bipartite graphs but also to more graph structures with complete bipartite subgraphs, which will provide potential applications for quantum information processing.
We propose a scheme for perfect transfer of an unknown qubit state via the discrete-time quantum walk on a line or a circle. For this purpose, we introduce an additional coin operator which is applied at the end of the walk. This operator does not depend on the state to be transferred. We show that perfect state transfer over an arbitrary distance can be achieved only if the walk is driven by an identity or a flip coin operator. Other biased coin operators and the Hadamard coin allow perfect state transfer over finite distances only. Furthermore, we show that quantum walks ending with a perfect state transfer are periodic.
We propose a scheme for perfect transfer of an unknown qubit state via the discrete-time quantum walk on a line or a circle. For this purpose, we introduce an additional coin operator which is applied at the end of the walk. This operator does not depend on the state to be transferred. We show that perfect state transfer over an arbitrary distance can be achieved only if the walk is driven by an identity or a flip coin operator. Other biased coin operators and the Hadamard coin allow perfect state transfer over finite distances only. Furthermore, we show that quantum walks ending with a perfect state transfer are periodic.
Abstract Quantum state transfer is an important task for scalable quantum complex networks. By selecting quantum walks with two coins as the basic model and two coin spaces as the communication carriers, we successfully implement some perfect state transfer tasks on various graphs (Shang et al 2019 Europhys. Lett. 124 60009). Here, we provide the first experimental realization of this scheme by IBM Quantum Experience platform. Especially, we demonstrate the transfer of Bell state, GHZ state and W state on complete graph through this quantum apparatus. Furthermore, we notice that our protocols have high fidelity by performing quantum state tomography.
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 mmm 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.