Quantum Squeeziness: Information-Theoretic Foundations of Quantum Software Testability

Abstract

Testability—the degree to which faults can be revealed and diagnosed—has long been fundamental in software engineering but remains largely unexplored for quantum software. This work presents the first formalisation of testability for quantum programs, adapting classical concepts to quantum computation. We introduce Quantum Squeeziness, an information-theoretic metric inspired by classical squeeziness, to quantify how faults are masked and prevented from propagating to observable outcomes. We treat it as an inverse measure of testability: higher squeeziness implies stronger fault masking and reduced detectability. We propose an efficient method to compute Quantum Squeeziness and validate it through large-scale quantum mutation analysis. Across more than 50k mutants, we observe a strong negative correlation between squeeziness and mutation score, showing that higher squeeziness predicts lower testability. We further introduce a technique that constrains where and how perturbations are injected, reducing cost while preserving accuracy. The computation is 15% faster than a standard error-propagation baseline, while the optimised variant, FastSqueeziness, reduces mean runtime from 3200 s to 189 s (16.9×speedup) with 95% accuracy. By establishing a rigorous foundation of testability for quantum software, this work opens new directions at the intersection of software engineering, quantum information theory, and testing. Beyond testing and debugging, it also supports applications in quantum error mitigation and correction, enabling principled assessment and improvement of program robustness.