The necessary and sufficient conditions when global and local fidelities are equal

In the field of quantum information theory, the concept of quantum fidelity is employed to quantify the similarity between two quantum states. It has been observed that the fidelity between two states describing a bipartite quantum system \(A \otimes B\) is always less than or equal to the quantum f...

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Bibliographic Details
Published inarXiv.org
Main Authors Seong-Kun, Kim, Lee, Yonghae
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 31.07.2023
Subjects
Accuracy
Information theory
Mathematics - Mathematical Physics
Physics - Mathematical Physics
Physics - Quantum Physics
Quantum phenomena
Quantum theory
Subsystems
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Summary:In the field of quantum information theory, the concept of quantum fidelity is employed to quantify the similarity between two quantum states. It has been observed that the fidelity between two states describing a bipartite quantum system \(A \otimes B\) is always less than or equal to the quantum fidelity between the states in subsystem \(A\) alone. While this fidelity inequality is well understood, determining the conditions under which the inequality becomes an equality remains an open question. In this paper, we present the necessary and sufficient conditions for the equality of fidelities between a bipartite system \(A \otimes B\) and subsystem \(A\), considering pure quantum states. Moreover, we provide explicit representations of quantum states that satisfy the fidelity equality, based on our derived results.
ISSN:2331-8422
DOI:10.48550/arxiv.2307.11310