Nonclassicality and Coherent Error Detection via Pseudo-Entropy

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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>S</mi><mo>ˇ</mo></mover></semantics></math></inline-formula>, focusing on its imaginary part <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>ℑ</mo><mover accent="true"><mi>S</mi><mo>ˇ</mo></mover></mrow></semantics></math></inline-formula> 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.