Quantum Interference-Induced Bhattacharyya Distance

• URL: http://arxiv.org/abs/2601.05749v1
• Date: Fri, 09 Jan 2026 12:05:04 GMT
• Title: Quantum Interference-Induced Bhattacharyya Distance
• Authors: Mostafizur Rahaman Laskar,
• Abstract summary: We propose a quantum distance measure between probability distributions encoded in quantum states based on the fragility of quantum interference under entangling evolution.<n>The Quantum Interference-Induced Bhattacharyya Distance (QIBD) is defined through a single-ancilla interferometric circuit.
• Score: 0.8122270502556374
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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