# Nonclassicality and Coherent Error Detection via Pseudo-Entropy

## TL;DR

This paper introduces a new method using pseudo-entropy to detect nonclassical behavior and coherent errors in quantum circuits, offering practical insights for quantum computing.

## Contribution

The paper introduces pseudo-entropy as a novel diagnostic tool for detecting nonclassicality and coherent errors in quantum circuits.

## Key findings

- The imaginary part of pseudo-entropy effectively identifies phase-coherent errors in quantum circuits.
- 55% of the parameter space remains classified as classical-like at hardware-calibrated sensitivity levels.
- The method is robust to noise and outperforms standard entropy-based approaches in simulations.

## Abstract

Pseudo-entropy is a complex-valued generalization of entanglement entropy defined on non-Hermitian transition operators and induced by post-selection. We present a simulation-based protocol for detecting nonclassicality and coherent errors in quantum circuits using this pseudo-entropy measure Sˇ, focusing on its imaginary part ℑSˇ as a diagnostic tool. Our method enables resource-efficient classification of phase-coherent errors, such as those from miscalibrated CNOT gates, even under realistic noise conditions. By quantifying the transition between classical-like and quantum-like behavior through threshold analysis, we provide theoretical benchmarks for error classification that can inform hardware calibration strategies. Numerical simulations demonstrate that 55% of the parameter space remains classified as classical-like (below classification thresholds) at hardware-calibrated sensitivity levels, with statistical significance confirmed through rigorous sensitivity analysis. Robustness to noise and comparison with standard entropy-based methods are demonstrated in a simulation. While hardware validation remains necessary, this work bridges theoretical concepts of nonclassicality with practical quantum error classification frameworks, providing a foundation for experimental quantum computing applications.