STM Journals Peer-reviewed research from Consortium e-Learning Network

Emerging Trends in Symmetry Review Article

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

  1. Tejas Bhushan N.B. Department of Chemistry, Regional Institute of Education (NCERT)
  2. Mohammed Almakki School of Engineering, Architecture and Interior Design, Amity University Dubai
  3. Mohammed El Khider Department of General Undergraduate Curriculum Requirements, University of Dubai

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

References (25)

  1. Zadeh LA. Fuzzy sets. Information and Control. 1965;8(3):338-353. doi:10.1016/s0019-9958(65)90241-x
  2. Atanassov KT. Intuitionistic fuzzy sets. Fuzzy Sets and Systems. 1986;20(1):87-96. doi:10.1016/s0165-0114(86)80034-3
  3. Feynman RP. Simulating physics with computers. International Journal of Theoretical Physics. 1982;21(6-7):467-488. doi:10.1007/bf02650179
  4. Acampora G. Quantum machine intelligence. Quantum Machine Intelligence. 2019;1(1-2):1-3. doi:10.1007/s42484-019-00006-5
  5. Ladd TD, Jelezko F, Laflamme R, Nakamura Y, Monroe C, O’Brien JL. Quantum computers. Nature. 2010;464(7285):45-53. doi:10.1038/nature08812
  6. Aaronson S. Read the fine print. Nature Physics. 2015;11(4):291-293. doi:10.1038/nphys3272
  7. Preskill J. Quantum Computing in the NISQ era and beyond. Quantum. 2018;2:79. doi:10.22331/q-2018-08-06-79
  8. Yogeesh N, Girija DK, Rashmi M, Divyashree J. Quantum implementation of fuzzy logic conjunction and disjunction using multi-qubit gates. Eur Chem Bull. 2023;12(7):137. doi:10.48047/ecb/2023.12.7.137.
  9. Yogeesh N. Intuitionistic Fuzzy Hypergraphs and Their Operations. Applied Computer Vision and Soft Computing with Interpretable AI. 2023:153-165. doi:10.1201/9781003359456-10
  10. Yogeesh N. INTUITIONISTIC FUZZY SCORING FOR FLUENCY IN TELEPRACTICE SESSIONS. International Journal of Applied Mathematics. 2025;38(3s):1078-1113. doi:10.12732/ijam.v38i3s.206
  11. Suleiman Mohammad, Yogeesh N, Khaleel Ibrahim Al-Daoud, N Raja, Manoj C R, Raghavendra M H, Asokan Vasudevan, et al. A Mathematical Fuzzy Model for Syntax-Pragmatics Interface. Forum for Linguistic Studies. 2025;7(6). doi:10.30564/fls.v7i6.9618
  12. Yogeesh N, Girija DK, William P, Rashmi M. Improving Speech Privacy with Fuzzy Logic-Based Encryption. 2023 IEEE 2nd International Conference on Industrial Electronics: Developments & Applications (ICIDeA). 2023:217-222. doi:10.1109/icidea59866.2023.10295183
  13. M R, N Y, K GD, William P. Robust Speech Processing with Fuzzy Logic-Driven Anti-Spoofing Techniques. 2023 International Conference on Self Sustainable Artificial Intelligence Systems (ICSSAS). 2023:1588-1594. doi:10.1109/icssas57918.2023.10331804
  14. Yogeesh N, Raja N. Fuzzy logic-based beat tracking in music signals. GI Forum. 2023;11(1):Article 343. doi:10.15463/gfbm-mib-2023–343.
  15. N Y, KARTHIK M, VASUDEVAN A, N S C, EU HUI S, TAFARA MUDZENGI M, et al. GLOBAL BIFURCATION FOR NONLINEAR OPERATORS WITH UNCERTAINTY BANDS. Global and Stochastic Analysis. 2025;12(06):44-60. doi:10.64837/gsa.12.6.5
  16. VASUDEVAN A, N Y, ALMAKKI M, SUNITHA MS, JOHN S, MUDZENGI MT. INVARIANT MANIFOLDS FOR NONLINEAR FLOWS WITH UNCERTAINTY-AWARE CONE CONDITIONS. Global and Stochastic Analysis. 2026;13(01):01-15. doi:10.64837/gsa.13.1.1
  17. Yogeesh N. Applying Fuzzy Data Science in Generative AI for Healthcare. Generative AI. 2025:215-248. doi:10.1002/9781394302932.ch10
  18. Aburub FAF, N Y, Mohammad SIS, Raja N, Lingaraju L, William P, et al. A Comprehensive Algebraic Framework for Fuzzy Graphs and Their Operators. Journal of Posthumanism. 2024;4(3). doi:10.63332/joph.v4i3.430
  19. From Crisp to Fuzzy: A Comparative Review of Statistical and Fuzzy Approaches to Problem Solving. Applied Mathematics & Information Sciences. 2025;19(3):647-658. doi:10.18576/amis/190313
  20. The Synergy of Simplicity and Vagueness: Exploring Simple Statistics in Fuzzy Mathematical Frameworks. Applied Mathematics & Information Sciences. 2025;19(2):457-465. doi:10.18576/amis/190219
  21. Yogeesh N. Fuzzy Logic in Metaverse Technology Roadmap. Metaverse for Sustainable Development. 2025:359-380. doi:10.1002/9781394272228.ch14
  22. Abdullahi Saleh I, Srivastava A. Exploring the Intersection of Fuzzy Logic and Quantum Logic: A New Frontier in Non-Classical Logics. SciWaveBulletin. 2023;01(02):27-34. doi:10.61925/swb.2023.1204
  23. Samaila B, Sekar C. Quantum Power Flow: Revolutionizing Power Systems Analysis. SciWaveBulletin. 2023;01(02):01-09. doi:10.61925/swb.2023.1201
  24. Giruba M, Saleh Al Ansari M. Quantum Field Theory: Advanced Calculations in Nonperturbative Regimes. SciWaveBulletin. 2023;01(04):01-08. doi:10.61925/swb.2023.1401
  25. Bellman RE, Zadeh LA. Decision-Making in a Fuzzy Environment. Management Science. 1970;17(4):B-141-B-164. doi:10.1287/mnsc.17.4.b141
Support