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Trace-Distance based End-to-End Entanglement Fidelity with Information Preservation in Quantum Networks

Pankaj Kumar, Binayak Kar, Shan-Hsiang Shen

TL;DR

This work introduced the trace-distance based path purification (TDPP) algorithm, specifically designed to enable information preservation and path purification entanglement routing, and identifies the shortest path within quantum networks using closeness centrality.

Abstract

Quantum networks hold the potential to revolutionize a variety of fields by surpassing the capabilities of their classical counterparts. Many of these applications necessitate the sharing of high-fidelity entangled pairs among communicating parties. However, the inherent nature of entanglement leads to an exponential decrease in fidelity as the distance between quantum nodes increases. This phenomenon makes it challenging to generate high-fidelity entangled pairs and preserve information in quantum networks. To tackle this problem, we utilized two strategies to ensure high-fidelity entangled pairs and information preservation within a quantum network. First, we use closeness centrality as a metric to identify the closest nodes in the network. Second, we introduced the trace-distance based path purification (TDPP) algorithm, specifically designed to enable information preservation and path purification entanglement routing. This algorithm identifies the shortest path within quantum networks using closeness centrality and integrates trace-distance computations for distinguishing quantum states and maintaining end-to-end (E2E) entanglement fidelity. Simulation results demonstrate that the proposed algorithm improves network throughput and E2E fidelity while preserving information compared to existing methods.

Trace-Distance based End-to-End Entanglement Fidelity with Information Preservation in Quantum Networks

TL;DR

This work introduced the trace-distance based path purification (TDPP) algorithm, specifically designed to enable information preservation and path purification entanglement routing, and identifies the shortest path within quantum networks using closeness centrality.

Abstract

Quantum networks hold the potential to revolutionize a variety of fields by surpassing the capabilities of their classical counterparts. Many of these applications necessitate the sharing of high-fidelity entangled pairs among communicating parties. However, the inherent nature of entanglement leads to an exponential decrease in fidelity as the distance between quantum nodes increases. This phenomenon makes it challenging to generate high-fidelity entangled pairs and preserve information in quantum networks. To tackle this problem, we utilized two strategies to ensure high-fidelity entangled pairs and information preservation within a quantum network. First, we use closeness centrality as a metric to identify the closest nodes in the network. Second, we introduced the trace-distance based path purification (TDPP) algorithm, specifically designed to enable information preservation and path purification entanglement routing. This algorithm identifies the shortest path within quantum networks using closeness centrality and integrates trace-distance computations for distinguishing quantum states and maintaining end-to-end (E2E) entanglement fidelity. Simulation results demonstrate that the proposed algorithm improves network throughput and E2E fidelity while preserving information compared to existing methods.

Paper Structure

This paper contains 13 sections, 2 theorems, 34 equations, 5 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Background of Quantum Network and Communication
  4. Network Topology and Notations
  5. Quantum Trace-Distance Measure and Operations
  6. Quantum Network Routing Design
  7. Information Preservation Quantification in Quantum Links
  8. Trace-Distance based Path Purification Algorithm
  9. Performance Analysis
  10. Simulation Methodology
  11. Fidelity Performance Trade-off Analysis
  12. Throughput Performance Analysis
  13. Conclusions

Key Result

Lemma 1

If in a quantum network, as shown in Figure fig.fig1, each node has a density matrix, denoted as $\rho_i$ for quantum state $\left|\psi\right\rangle$ and $\sigma_i$ for quantum state $\left|\varphi\right\rangle$, then the fidelity between $\rho_i$ and $\sigma_i$ is defined as the maximum value of th

Figures (5)

  • Figure 1: llustration of information transmission in a quantum network, where $\rho_i$ is the density matrix of quantum state at the source node and $\sigma_i$ is the density matrix of the quantum state received at adjacent node respectively.
  • Figure 2: Entanglement purification using pumping process. In this process, quantum nodes initially generate low-fidelity EPR pairs, such as $\rho_i$ = $0.528$ and $\sigma_i$ = $0.548$. Once these pairs are generated, we apply the entanglement pumping process, using \ref{['eq-fidelity']}, to purify the fidelity to $0.731$ in the first round. In the second round, we combine the newly purified fidelity with the base fidelity of $0.548$ to further purify the fidelity to $0.793$. This process is repeated in the next round, the fidelity is purified to $0.809$ which is greater than the desired fidelity threshold.
  • Figure 3: Trace-distance based quantum network routing architecture, where fidelity values are indicated in red, trace-distance in black, and the closeness centrality of each node in purple.
  • Figure 4: Fidelity performance comparison of multiple S-D pairs in communication networks.
  • Figure 5: Throughput-performance comparison of multiple S-D pairs in communication networks.

Theorems & Definitions (5)

  • Lemma 1
  • proof
  • Theorem 1
  • proof
  • proof