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Mathematics

Hierarchical Quantum Information Splitting of an Arbitrary Two-Qubit State Based on a Decision Tree

Dongfen Li, Yundan Zheng, Xiaofang Liu, Jie Zhou, Yuqiao Tan, Xiaolong Yang, Mingzhe Liu

Published Dec 2, 2022• 4 citations
Publisher

Abstract

Quantum informatics is a new subject formed by the intersection of quantum mechanics and informatics. Quantum communication is a new way to transmit quantum states through quantum entanglement, quantum teleportation, and quantum information splitting. Based on the research of multiparticle state quantum information splitting, this paper innovatively combines the decision tree algorithm of machine learning with quantum communication to solve the problem of channel particle allocation in quantum communication, and experiments showed that the algorithm can make the optimal allocation scheme. Based on this scheme, we propose a two-particle state hierarchical quantum information splitting scheme based on the multi-particle state. First, Alice measures the Bell states of the particles she owns and tells the result to the receiver through the classical channel. If the receiver is a high-level communicator, he only needs the help of one of the low-level communicators and all the high-level communicators. After performing a single particle measurement on the z-basis, they send the result to the receiver through the classical channel. When the receiver is a low-level communicator, all communicators need to measure the particles they own and tell the receiver the results. Finally, the receiver performs the corresponding unitary operation according to the received results. In this regard, a complete hierarchical quantum information splitting operation is completed. On the basis of theoretical research, we also carried out experimental verification, security analysis, and comparative analysis, which shows that our scheme is reliable and has high security and efficiency.

DOI
10.3390/math10234571

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Quantum informatics is a new subject formed by the intersection of quantum mechanics and informatics. Quantum communication is a new way to transmit quantum states through quantum entanglement, quantum teleportation, and quantum information splitting. Based on the research of multiparticle state quantum information splitting, this paper innovatively combines the decision tree algorithm of machine learning with quantum communication to solve the problem of channel particle allocation in quantum communication, and experiments showed that the algorithm can make the optimal allocation scheme. Based on this scheme, we propose a two-particle state hierarchical quantum information splitting scheme based on the multi-particle state. First, Alice measures the Bell states of the particles she owns and tells the result to the receiver through the classical channel. If the receiver is a high-level communicator, he only needs the help of one of the low-level communicators and all the high-level communicators. After performing a single particle measurement on the z-basis, they send the result to the receiver through the classical channel. When the receiver is a low-level communicator, all communicators need to measure the particles they own and tell the receiver the results. Finally, the receiver performs the corresponding unitary operation according to the received results. In this regard, a complete hierarchical quantum information splitting operation is completed. On the basis of theoretical research, we also carried out experimental verification, security analysis, and comparative analysis, which shows that our scheme is reliable and has high security and efficiency.
With the emergence of classical communication security problems, quantum communication has been studied more extensively. In this paper, a novel probabilistic hierarchical quantum information splitting protocol is designed by using a non-maximally entangled four-qubit cluster state. Firstly, the sender Alice splits and teleports an arbitrary one-qubit secret state invisibly to three remote agents Bob, Charlie, and David. One agent David is in high grade, the other two agents Bob and Charlie are in low grade. Secondly, the receiver in high grade needs the assistance of one agent in low grade, while the receiver in low grade needs the aid of all agents. While introducing an ancillary qubit, the receiver’s state can be inferred from the POVM measurement result of the ancillary qubit. Finally, with the help of other agents, the receiver can recover the secret state probabilistically by performing certain unitary operation on his own qubit. In addition, the security of the protocol under eavesdropping attacks is analyzed. In this proposed protocol, the agents need only single-qubit measurements to achieve probabilistic hierarchical quantum information splitting, which has appealing advantages in actual experiments. Such a probabilistic hierarchical quantum information splitting protocol hierarchical is expected to be more practical in multipartite quantum cryptography.
Quantum information splitting (QIS) provides an idea for transmitting the quantum state through a classical channel and a preshared quantum entanglement resource. This paper presents a new scheme for QIS based on a five-qubit cluster state and a Bell state. In this scheme, the sender transmits the unknown three-qubit secret state to two agents by the quantum channel with the Bell basis measurement three times and broadcasts the measurement results to the agents through the classical channel. The agent who restores the secret state can successfully recover the initial information to be transmitted through the appropriate unitary operation with the help of the other party. Firstly, our scheme's process can be accurately realized by performing the applicable Bell basis measurement, single-qubit measurement, and local unitary operation instead of a multiparticle joint measurement. The splitting process of quantum information is realized through a convenient operation. Secondly, compared with some previous schemes, the efficiency of the total scheme has been improved in principle, and the qubit consumption is reduced. Finally, the security of the quantum information splitting scheme is analyzed from the perspectives of external attacks and participant attacks. It is proved that our scheme can effectively resist internal participant attacks and external eavesdropper attacks.
Through introducing the new application of a genuinely entangled six-qubit state,quantum information splitting of an arbitrary two-qubit state was investigated.For the quantum information splitting,a genuinely entangled six-qubit state was shared by a sender(Alice),a controller(Charlie) and a receiver(Bob).The sender firstly performed twice Bell-state measurements,and then the controller made a Bell-state measurement.Finally the receiver can reconstruct the arbitrary two-qubit state by performing some appropriate unitary transformations on his qubits after he knew the measured results of both the sender and the controller.This quantum information splitting scheme is deterministic,i.e.the probability of success is 100%.In comparison with the quantum information splitting scheme using the same quantum channel the sender and the controller only need to perform Bell-state measurements,not joint multi-qubit measurement,which makes this scheme simpler and easier,and can be fulfilled based on present experimental technology.
A scheme is proposed for quantum information splitting of a two-qubit Bell state by using a four-qubit entangled state as a quantum channel. In the scenario, it is supposed that there are three legitimate parties, say Alice, Bob and Charlie. Alice is the sender of quantum information. Bob and Charlie are two agents. Alice first performs GHZ state measurement and tells Bob and Charlie the measurement results via a classical channel. It is impossible for Bob to reconstruct the original state with local operations unless help is obtained from Charlie. If Charlie allows Bob to reconstruct the original state information, he needs to perform a single-qubit measurement and tell Bob the measurement result. Using the measurement results from Alice and Charlie, Bob can reconstruct the original state. We also consider the problem of security attacks. This protocol is considered to be secure.
Quantum teleportation is a unique quantum information processing method in quantum communication. Researchers have shown considerable interest in hierarchically controlled teleportation by using quantum entangled states as the quantum channel. Protocols for the hierarchically controlled teleportation of an arbitrary single-qubit via a four-qubit χ state and a four-qubit cluster state have been proposed. We present a protocol for the hierarchically controlled teleportation of an arbitrary m-qudit (d-dimensional quantum system) state by using a partially entangled quantum state as the quantum channel. The sender performs m generalized Bell-state measurements on her 2m particles. To reconstruct the original state, the upper-grade receiver only needs to apply a unitary operation in accordance with one of the receivers’ measurement results, and the lower-grade receivers need to perform a unitary operation according to all the other receivers’ measurement results. The receivers can reconstruct the original state probabilistically by introducing an auxiliary qubit and performing a collective unitary transformation. The protocol has the advantage of having high channel capacity by using a high-dimensional entangled state as the quantum channel.
By utilizing the non-maximally entangled four-qubit cluster states as the quantum channel, we first propose a hierarchical quantum information splitting scheme of arbitrary three-qubit states among three agents with a certain probability. Then we generalize the scheme to arbitrary multi-qubit states. Hierarchy is reflected on the different abilities of agents to restore the target state. The high-grade agent only needs the help of one low-grade agent, while the low-grade agent requires all the other agents' assistance. The designated receiver performs positive operator-valued measurement (POVM) which is elaborately constructed with the aid of Hadamard matrix. It is worth mentioning that a general expression of recovery operation is derived to disclose the relationship with measurement outcomes. Moreover, the scheme is extended to multiple agents by means of the symmetry of cluster states.