  Quantum state comparison, utilizing metrics like fidelity and trace distance,
underpins the assessment of quantum networks within quantum information theory.
While recent research has expanded theoretical understanding, incorporating
error analysis and scalability considerations remains crucial for practical
applications. The primary contribution of this letter is to address these gaps
by deriving the novel operational trace distance for multi-node networks,
establishing a trace distance vs. fidelity benchmark incorporating error
bounds, and bridging quantum operations with tensor network analysis. We
further explore the application of tensor network tools to quantum networks,
offering new analytical avenues. This comprehensive approach provides a robust
framework for evaluating quantum network performance under realistic error
conditions, facilitating the development of reliable quantum technologies.
