Quantum-Fuzzy Tensor Operators and Uncertainty-Band Bifurcation for Symmetry-Preserving State Discrimination

Year : 2026 | Volume : 02 | Issue : 01 | Page : 08 15
    By

    Tejas Bhushan N.B.,

  • Mohammed Almakki,

  • Mohammed El Khider,

  1. Research Student, Department of Chemistry, Regional Institute of Education (NCERT), Karnataka, India
  2. Assistant Professor, School of Engineering, Architecture and Interior Design, Amity University Dubai, Dubai, United Arab Emirates
  3. Assistant Professor, Department of General Undergraduate Curriculum Requirements, University of Dubai, Dubai, United Arab Emirates

Abstract

A tensor-operator framework is developed for fuzzy conjunction, fuzzy disjunction, and symmetry-preserving state discrimination in multi-qubit quantum systems. In this formulation, fuzzy membership and non-membership degrees are represented through expectations of effect operators acting on density matrices, providing a natural bridge between fuzzy logic and quantum measurement theory. Conjunction and disjunction operations are extended to the quantum domain via tensorised channels, constructed using projective measurements and unitary transformations, enabling logical aggregation directly on composite quantum states. To incorporate structural constraints, permutation-group symmetry is enforced through an operator-valued projector acting on the joint Hilbert space. This leads to the definition of a symmetry-defect functional, which quantifies deviations from exact invariance under qubit permutations. The framework thus separates symmetric components of the state from symmetry-breaking residuals, allowing controlled manipulation of both. An uncertainty-band family of perturbed quantum channels is introduced to model variability and noise in practical systems. Within this setting, fixed-point conditions are derived in operator form, characterizing states that remain invariant under repeated channel application. Furthermore, local bifurcation analysis reveals how qualitative changes in system behavior arise when channel parameters vary. In particular, the resulting branch equations show that nontrivial discrimination states emerge when a dominant eigenvalue of the channel crosses unity, signaling a transition from trivial to informative solutions. Illustrative two- and three-qubit examples demonstrate the practical implications of the theory. These cases show that small, controlled symmetry-breaking perturbations can enhance state discrimination performance while maintaining bounded symmetry loss. This highlights a key trade-off between symmetry preservation and functional effectiveness. Overall, the proposed framework provides a mathematically rigorous contribution in the RTM style, integrating tensor algebra, quantum channels, fuzzy logic, and uncertainty-band analysis. It offers a unified perspective for designing and analyzing symmetry-aware quantum information processes with controlled uncertainty.

Keywords: Quantum fuzzy logic; tensor operators; bifurcation; symmetry projector; multi-qubit gates; state discrimination

[This article belongs to Emerging Trends in Symmetry ]

How to cite this article:
Tejas Bhushan N.B., Mohammed Almakki, Mohammed El Khider. Quantum-Fuzzy Tensor Operators and Uncertainty-Band Bifurcation for Symmetry-Preserving State Discrimination. Emerging Trends in Symmetry. 2026; 02(01):08-15.
How to cite this URL:
Tejas Bhushan N.B., Mohammed Almakki, Mohammed El Khider. Quantum-Fuzzy Tensor Operators and Uncertainty-Band Bifurcation for Symmetry-Preserving State Discrimination. Emerging Trends in Symmetry. 2026; 02(01):08-15. Available from: https://journals.stmjournals.com/etsy/article=2026/view=247454


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Regular Issue Subscription Review Article
Volume 02
Issue 01
Received 14/03/2026
Accepted 22/04/2026
Published 30/04/2026
Publication Time 47 Days
4

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