Hierarchical Quantum Information Splitting of an Arbitrary Two-Qubit State Based on a Decision Tree
Abstract
:1. Introduction
2. Overall Design of the Scheme
- (1)
- First, use the decision tree algorithm to make the optimal communication decision for channel particle allocation.
- (2)
- Then, we assume that Alice is the sender; and the communication participants are Bob1, Bob2, Charlie1, Charlie2, and Charlie3. According to the decision, Bob1 and Bob2 are high-level communicators, and Charlie1, Charlie2, and Charlie3 are low-level communicators. Different receivers have different particle distribution schemes.
- (3)
- Next, Alice conducts Bell-state measurement on the particle pair (A, 1), (B, 2). When the receiver is a high-level communicator, only one of Bob2 and a low-level communicator is required to perform a Z-based single particle measurement; after the measurement operation is performed, the result is reported to the receiver through the classical channel. When the receiver is a low-level communicator, all communication participants need to perform the measurement, and the low-level communicator needs to perform X-based single-particle measurements. Then, the communicator sends the result to the receiver.
- (4)
- Finally, after receiving all the measurement results, the receiver conducts a unitary operation on the collapsed state using the corresponding results. It can recover any two-qubit state information that Alice intends to send.
3. An Optimal Allocation Model of Channel Particles Based on a Decision Tree
3.1. Data Preprocessing
3.2. Model Establishment and Evaluation Analysis
3.3. Optimal Allocation Model of Channel Particles
4. Hierarchical Quantum Information Splitting Scheme for Arbitrary Two-Qubit State Based on Multi-Qubit State
4.1. Information Splitting When Receiver Authority Is High
4.2. Information Splitting When Receiver Authority Is Low
4.3. The Hierarchical Quantum Information Splitting Protocol Based on N-Party
5. Experiment and Analysis
5.1. Experiments on Hierarchical Quantum Information Splitting Schemes
5.2. Security Analysis
5.3. Scheme Comparison Analysis
6. Discussion
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Model | Resampling Error | Cross-Validation Error |
---|---|---|
Model 1 | 0 | 0 |
Model 1(a) | 0.002 | 0.002 |
Model | Resampling Error | Cross-Validation Error |
---|---|---|
Model 2 | 0.007 | 0.009 |
Model 2(a) | 0.015 | 0.015 |
Model 2(b) | 0.007 | 0.01 |
Model | Resampling Error | Cross-Validation Error |
---|---|---|
Model 3(a) | 0.009 | 0.015 |
Model 3(b) | 0.018 | 0.021 |
Model 3(c) | 0.01 | 0.016 |
The Measurement of Alice | The Collapse State after Measurement |
---|---|
Measurement Results of Bob2, Charlie1, Charlie2 and Charlie3 1 | The State Obtained by Bob1 | Unitary Operation |
---|---|---|
Alice’s Measurements | Measurement Results of Bob1 and Bob2 | Measurement Results of Charlie2 and Charlie3 | Unitary Operation |
---|---|---|---|
States | Shots | Frequency (%) |
---|---|---|
2072 | 25.3% | |
1999 | 24.4% | |
2114 | 25.8% | |
2007 | 24.5% |
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Li, D.; Zheng, Y.; Liu, X.; Zhou, J.; Tan, Y.; Yang, X.; Liu, M. Hierarchical Quantum Information Splitting of an Arbitrary Two-Qubit State Based on a Decision Tree. Mathematics 2022, 10, 4571. https://doi.org/10.3390/math10234571
Li D, Zheng Y, Liu X, Zhou J, Tan Y, Yang X, Liu M. Hierarchical Quantum Information Splitting of an Arbitrary Two-Qubit State Based on a Decision Tree. Mathematics. 2022; 10(23):4571. https://doi.org/10.3390/math10234571
Chicago/Turabian StyleLi, Dongfen, Yundan Zheng, Xiaofang Liu, Jie Zhou, Yuqiao Tan, Xiaolong Yang, and Mingzhe Liu. 2022. "Hierarchical Quantum Information Splitting of an Arbitrary Two-Qubit State Based on a Decision Tree" Mathematics 10, no. 23: 4571. https://doi.org/10.3390/math10234571