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quant-ph2025
Fixed Points in Quantum Metric Spaces: A Structural Advantage over Fuzzy Frameworks
Nicola Fabiano
We prove an existence and uniqueness theorem for fixed points of contraction maps in the framework of quantum metric spaces, where distinguishability is defined by the norm:…
quant-ph2025
On the Incompatibility of Quantum State Geometry and Fuzzy Metric Spaces: Three No-Go Theorems
Nicola Fabiano
We prove three structural impossibility results demonstrating that fuzzy metric spaces cannot capture essential features of quantum state geometry. First, we show they cannot model…
quant-ph2025
Quantum Metric Spaces: Replacing Fuzzy Metrics with the Hilbert Space Structure of Quantum States
Nicola Fabiano
Fuzzy metric spaces, grounded in t-norms and membership functions, have been widely proposed to model uncertainty in machine learning, decision systems, and artificial intelligence…