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arXiv:2501.11785

Quantum communication scheme to teleport arbitrary quantum state via discrete time quantum walks

Rachana Soni, Neelam Choudhary, Neha Singh

Published Jan 20, 2025• 0 citations
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Abstract

In this article, we propose a quantum communication protocol via 2-step discrete time quantum walks with two coins on a graph of 10 vertices containing both cycles and paths. Quantum walks are known for their ability to integrate quantum mechanics dynamics like superposition and entanglement during the procedure. We calculate the total final quantum state of the system as well as the recovery operators to rescue the initial quantum state back at the receiver's location. Our work provides a fundamental block for a quantum teleportation scheme on a specific series of cycle and path graphs.

DOI
10.48550/arxiv.2501.11785

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In this article, we propose a quantum communication protocol via 2-step discrete time quantum walks with two coins on a graph of 10 vertices containing both cycles and paths. Quantum walks are known for their ability to integrate quantum mechanics dynamics like superposition and entanglement during the procedure. We calculate the total final quantum state of the system as well as the recovery operators to rescue the initial quantum state back at the receiver's location. Our work provides a fundamental block for a quantum teleportation scheme on a specific series of cycle and path graphs.
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.
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.
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.
Perfect state transfer between two marked vertices of a graph by means of a discrete-time quantum walk is analyzed. We consider the quantum walk search algorithm with two marked vertices, sender and receiver. It is shown by explicit calculation that, for the coined quantum walks on a star graph and a complete graph with self-loops, perfect state transfer between the sender and receiver vertex is achieved for an arbitrary number of vertices NNN in O(N)O(\sqrt{N})O(N​) steps of the walk. Finally, we show that Szegedy's walk with queries on a complete graph allows for state transfer with unit fidelity in the limit of large NNN.
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.