Quantum Interference-Induced Bhattacharyya Distance

Abstract:We propose a quantum distance measure between probability distributions encoded in quantum states based on the fragility of quantum interference under entangling evolution. The Quantum Interference-Induced Bhattacharyya Distance (QIBD) is defined through a single-ancilla interferometric circuit in which an interaction Hamiltonian generates correlation-dependent phases that modulate interference visibility. When the interaction vanishes, QIBD reduces to the classical Bhattacharyya distance; however, for entangling interactions, it cannot be expressed as a function of fidelity alone. Numerical simulations demonstrate that QIBD responds to correlation structure in ways that overlap-based measures do not, suggesting potential utility in contexts where interaction-aligned correlations are physically relevant.

arXiv:2601.05749 [quant-ph]

(or arXiv:2601.05749v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2601.05749 Focus to learn more arXiv-issued DOI via DataCite

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