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Loss Tomography for Quantum Networks

Jake Navas, Jaden Brewer, Jaime Diaz, Matheus Guedes de Andrade, Don Towsley, Inès Montaño

TL;DR

This work shows how the analysis of quantum capacity regions can be used as a powerful new tool in quantum network tomography, and demonstrates how the loss on quantum channels in the network can be characterized directly from quantum capacity region diagrams, even in the presence of bit-flip errors.

Abstract

With steady progress in the development of quantum networks, the question on how to best provide end-to-end characterization of such networks (Quantum Network Tomography) is quickly becoming more pressing. Initial results demonstrated how we can utilize multipartite entanglement distribution to determine error probabilities of single-Pauli channels and depolarizing channels. In this work, we show how the analysis of quantum capacity regions can be used as a powerful new tool in quantum network tomography. As a first application of the proposed method, we demonstrate how we can characterize the loss on quantum channels in the network directly from quantum capacity region diagrams, even in the presence of bit-flip errors. Our results indicate that quantum capacity regions are not only valuable for network design, resource allocation, and protocol benchmarking, but also show promise for applications in quantum network tomography, particularly in loss tomography.

Loss Tomography for Quantum Networks

TL;DR

This work shows how the analysis of quantum capacity regions can be used as a powerful new tool in quantum network tomography, and demonstrates how the loss on quantum channels in the network can be characterized directly from quantum capacity region diagrams, even in the presence of bit-flip errors.

Abstract

With steady progress in the development of quantum networks, the question on how to best provide end-to-end characterization of such networks (Quantum Network Tomography) is quickly becoming more pressing. Initial results demonstrated how we can utilize multipartite entanglement distribution to determine error probabilities of single-Pauli channels and depolarizing channels. In this work, we show how the analysis of quantum capacity regions can be used as a powerful new tool in quantum network tomography. As a first application of the proposed method, we demonstrate how we can characterize the loss on quantum channels in the network directly from quantum capacity region diagrams, even in the presence of bit-flip errors. Our results indicate that quantum capacity regions are not only valuable for network design, resource allocation, and protocol benchmarking, but also show promise for applications in quantum network tomography, particularly in loss tomography.

Paper Structure

This paper contains 13 sections, 10 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Methods
  3. Model System and Network Simulation
  4. Extracting Quantum Capacity Regions
  5. Channel Noise
  6. Results
  7. Single Noisy Channel
  8. Noisy Root Channel
  9. Noisy Leaf Channels
  10. Homogeneous/Heterogeneous Noise Models
  11. Discussion
  12. Conclusion
  13. Acknowledgments

Figures (3)

  • Figure 1: (a) End-to-end entanglement path generated between $N_1$ and $N_2$ in red. Repeated for $N_1$ and $N_3$ in blue (b) Example capacity regions for an ideal, noiseless network (dashed) and a network with heterogeneous loss and bit-flip noise model (red).
  • Figure 2: Dashed black indicates the ideal, noiseless network. Blue: 15% probability of loss, red: 15% probability of bit-flip error, green: both loss and bit-flip errors at 15% each.
  • Figure 3: Dashed black indicates the ideal, noiseless network. Blue: all channels have 15% probability of loss, red: all channels have 10% probability of bit-flip error, green: $QC_1$ and $QC_2$ have 10% loss and 10% bit-flip, whereas $QC_3$ has 30% loss and 30% bit-flip