Amirov, Orhan; Celik, Necati; Karabacak, Mesut

In this study, we investigate the purity of density operators constructed from non-orthogonal quantum states. Starting from a general statistical mixture of normalized states, we derive an explicit expression for the purity in terms of the associated probability distribution and the pairwise overlaps between the states, quantified by |⟨ψi|ψj⟩|2. This formulation clearly separates the contributions arising from classical probability weights and quantum interference effects induced by non-orthogonality. To further analyze the impact of state overlaps, we introduce an average overlap quantity that captures the global contribution of non-orthogonal components. Based on this representation, we establish upper bounds for the purity using both global and local overlap parameters. In particular, we show that the purity can be effectively controlled by the maximum pairwise overlap, eliminating the need to compute all individual inner products explicitly. A refined bound is also obtained by incorporating local overlap measures, leading to a tighter characterization of the system. In addition, we develop a general framework connecting overlap-based purity bounds with quantum Fisher information (QFI) in parameter-dependent quantum systems. We show that the overlap structure can be used to indirectly control and estimate the behavior of QFI, especially in cases where direct spectral analysis is not tractable. The applicability of the proposed approach is demonstrated through an explicit example involving non-orthogonal qubit states. These results provide a practical framework for estimating the mixedness of quantum states and offer useful insights into the interplay between non-orthogonality, purity, and quantum Fisher information in quantum information theory.

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Şahin, Ridvan; Karabacak, Mesut

As a generation of Atanassov's intuitionistic fuzzy set, the single-valued neutrosophic set is an important modeling approach for expressing and processing the inconsistent and indeterminate information very well. Similarity measure is an important tool frequently used in a variety of areas, from clustering analysis to medical diagnosis. Although neutrosophic literature has many similarity measures, they have some disadvantages that do not provide the general conditions of the similarity measure for some specific values. In this chapter, we present a novel similarity measure to handle the relationship between two single-valued neutrosophic sets. It uses a matrix norm and a strictly increasing (or decreasing) binary function called fuzzy implication, and provides axiomatic definition properties of similarity measure. The advantage of using fuzzy implications is that it offers not only different final options to decision-makers but also gives a parameterized class of similarity measures of SVNSs. It is appeared that the developed similarity measure gives better results when compared to other existing similarity measures. Finally, several numerical examples related to pattern recognition, such as medical diagnosis and taxonomy approach, and clustering analysis are performed to demonstrate the practical applicability of the proposed similarity measure.

AtıfScopus17·OpenAlex14

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