Enhancing distributed sensing with imperfect error correction

TL;DR

This paper investigates how finite squeezed GKP states and various concatenation schemes can improve distributed quantum sensing performance under realistic noise conditions, balancing error correction and resource constraints.

Contribution

It introduces a balanced concatenation scheme for GKP codes that outperforms traditional methods in heterogeneous noise environments and analyzes the trade-offs in sensing tasks.

Findings

Balanced concatenation scheme outperforms sequential schemes with finite GKP squeezing.

Optimal energy distribution among sensors enhances parameter estimation.

Finite squeezed GKP codes significantly reduce error probability in hypothesis testing.

Abstract

Entanglement has shown promise in enhancing information processing tasks in a sensor network, via distributed quantum sensing protocols. As noise is ubiquitous in sensor networks, error correction schemes based on Gottesman, Kitaev and Preskill (GKP) states are required to enhance the performance, as shown in [New J. Phys. 22, 022001 (2020)] assuming homogeneous noise among sensors and perfect GKP states. Here, we extend the analyses of performance enhancement to finite squeezed GKP states in a heterogeneous noise model. To begin with, we study different concatenation schemes of GKP-two-mode-squeezing codes. While traditional sequential concatenation schemes in previous works do improve the suppression of noise, we propose a balanced concatenation scheme that outperforms the sequential scheme in presence of finite GKP squeezing. We then apply these results to two specific tasks in distributed quantum sensing -- parameter estimation and hypothesis testing -- to understand the trade-off between imperfect squeezing and performance. For the former task, we consider an energy-constrained scenario and provide an optimal way to distribute the energy of the finite squeezed GKP states among the sensors. For the latter task, we show that the error probability can still be drastically lowered via concatenation of realistic finite squeezed GKP codes.