Quantum Fisher Information Tensor and Diagnostic Metrics for Qubit Architectures: Towards Informational Nanotechnologies at the Nanoscale

Abstract

Quantum computing is increasingly regarded as a part of information nanotechnology, where reliable diagnostics under realistic noise conditions are crucial. Depolarization channels are commonly used as a fundamental model of quantum noise, but systematic diagnostic frameworks are still underdeveloped. We introduce a structured approach as to computational methods for depolarization channels, establish formal criteria such as metric reliability, and develop diagnostic maps and quantum Fisher information (QFI) tensors. Symbolic modelling of density matrices under noise allows for the analytical calculation of QFI components, revealing the isotropy and degeneracy of tensors at the critical point of Blochsphere collapse. Comparing quantum metrics, including purity, entropy, accuracy, Bloch norm, and Bloch-angle deviation (BAD), uncovers different sensitivities. Notably, purity and entropy reach their extremes with minimal uncertainty, while the Bloch norm and BAD quickly detect orientation loss and the inversion of the Bloch vector. The classification of subcritical Bloch-sphere compression, critical collapse, and supercritical inversion is validated, with BAD serving as an operational boundary marker. Potential applications include reliability testing in quantum processors, decoherence diagnostics in nanoscale devices, and benchmarking quantum gates. In Ukraine, this work is among the first systematic studies of a depolarizing quantum-noise channel, enhancing national expertise in diagnostic tools for quantum nanotechnology.