Quantum Interference-Induced Bhattacharyya Distance

TL;DR

This paper introduces a quantum distance measure called QIBD that leverages quantum interference to quantify differences between probability distributions encoded in quantum states, capturing correlation structures beyond classical measures.

Contribution

The paper presents the QIBD, a novel quantum distance measure based on interference fragility, which generalizes classical Bhattacharyya distance and responds uniquely to quantum correlations.

Findings

QIBD reduces to classical Bhattacharyya distance when interactions vanish.

QIBD responds distinctly to correlation structures compared to overlap-based measures.

Numerical simulations show QIBD's potential in detecting physically relevant quantum correlations.

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.