# Splitting an Arbitrary Three-Qubit State via a Five-Qubit Cluster State and a Bell State

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## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

#### 2.1. Basic Quantum Gates

#### 2.2. Cluster State

#### 2.3. The Preparation of the Five-Qubit Cluster State

- (1)
- Prepare the five individual single qubits $\left(a,b,c,d,e\right)$ in the states ${\left|0\right.\u232a}_{a}$, ${\left|0\right.\u232a}_{b}$, ${\left|0\right.\u232a}_{c}$, ${\left|0\right.\u232a}_{d}$, ${\left|0\right.\u232a}_{e}$, respectively.
- (2)
- Perform H gateon qubits $a$, $c$.
- (3)
- Carry out the CNOT gate on the qubit pairs $\left(a,b\right)$, $\left(c,d\right)$, $\left(a,c\right)$, and $\left(c,e\right)$, in which the control qubit is the former particle in the qubit pairs, and the target qubitis the second inputparticle, respectively.

## 3. Splitting an Arbitrary Three-Qubit State

**Step 1**Share the particles of quantum entangled states securely

**Step 2**Alison performs the Bell basis measurements

**Step 3**Calvin performs the single-qubit measurement

**Step 4**Bond reconstructs the state to be transmitted

## 4. Security and Efficiency

#### 4.1. Security Analysis

#### 4.1.1. Internal Participant Attack

#### 4.1.2. External Eavesdropper Attack

#### 4.2. Efficiency Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**The QIS process between the three parties. The particles connected by solid lines are in an entangled state. BM represents the Bell basis measurement, and SM represents the single-qubit measurement, U1, U3 and U7 represent unitary operations on the particles 1, 3 and 7, respectively. In the step 1 (

**a**), Alison, Bond and Calvin possess the particles 246, 137 and 5, respectively. In the step 2 (

**b**), Alison performs three times BM on her owned qubit pairs (x, 2), (y, 4) and (z, 6), respectively. In the step 3 (

**c**), Calvin performs SM on particle 5. In the step 4 (

**d**), Bond reconstructs the state to be transmitted through appropriate U1, U3 and U7 operations.

**Table 1.**The comparison for using the different quantum channels to split an arbitrary three-qubit state.

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**MDPI and ACS Style**

Xu, G.; Zhou, T.; Chen, X.-B.; Wang, X.
Splitting an Arbitrary Three-Qubit State via a Five-Qubit Cluster State and a Bell State. *Entropy* **2022**, *24*, 381.
https://doi.org/10.3390/e24030381

**AMA Style**

Xu G, Zhou T, Chen X-B, Wang X.
Splitting an Arbitrary Three-Qubit State via a Five-Qubit Cluster State and a Bell State. *Entropy*. 2022; 24(3):381.
https://doi.org/10.3390/e24030381

**Chicago/Turabian Style**

Xu, Gang, Tianai Zhou, Xiu-Bo Chen, and Xiaojun Wang.
2022. "Splitting an Arbitrary Three-Qubit State via a Five-Qubit Cluster State and a Bell State" *Entropy* 24, no. 3: 381.
https://doi.org/10.3390/e24030381