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Quantum Interference-Induced Bhattacharyya Distance

arXiv Quantum Physics
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⚡ Quantum Brief
A new quantum distance measure, QIBD, leverages interference fragility in entangled systems to compare probability distributions encoded in quantum states, offering a novel metric beyond classical fidelity-based approaches. The measure uses a single-ancilla interferometric circuit where an interaction Hamiltonian introduces correlation-dependent phases, directly modulating interference visibility to quantify distributional differences. QIBD collapses to the classical Bhattacharyya distance when interactions vanish but diverges for entangling cases, proving it cannot be reduced to fidelity alone—a key distinction from existing overlap-based metrics. Numerical simulations reveal QIBD’s unique sensitivity to correlation structures, capturing interaction-aligned patterns that traditional measures overlook, particularly in physically relevant quantum systems. The work suggests applications in quantum machine learning, metrology, and error mitigation, where interaction-dependent correlations play a critical role in system behavior and performance.
Quantum Interference-Induced Bhattacharyya Distance

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Quantum Physics arXiv:2601.05749 (quant-ph) [Submitted on 9 Jan 2026] Title:Quantum Interference-Induced Bhattacharyya Distance Authors:Mostafizur Rahaman Laskar View a PDF of the paper titled Quantum Interference-Induced Bhattacharyya Distance, by Mostafizur Rahaman Laskar View PDF HTML (experimental) 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. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.05749 [quant-ph] (or arXiv:2601.05749v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.05749 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Mostafizur Rahaman Laskar [view email] [v1] Fri, 9 Jan 2026 12:05:04 UTC (64 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum Interference-Induced Bhattacharyya Distance, by Mostafizur Rahaman LaskarView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)

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Source: arXiv Quantum Physics