Bipolar Quantum Logic Gates and Quantum Cellular Combinatorics—A Logical Extension to Quantum Entanglement

Wen-Ran Zhang^{*}

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Based on bipolar dynamic logic (BDL) and bipolar quantum linear algebra (BQLA) this work introduces bipolar quantum logic gates and quantum cellular combinatorics with a logical interpretation to quantum entanglement. It is shown that: 1) BDL leads to logically definable causality and generic particle-antiparticle bipolar quantum entanglement; 2) BQLA makes composite atom-atom bipolar quantum entanglement reachable. Certain logical equivalence is identified between the new interpretation and established ones. A logical reversibility theorem is presented for ubiquitous quantum computing. Physical reversibility is briefly discussed. It is shown that a bipolar matrix can be either a modular generalization of a quantum logic gate matrix or a cellular connectivity matrix. Based on this observation, a scalable graph theory of quantum cellular combinatorics is proposed. It is contended that this work constitutes an equilibrium-based logical extension to Bohr’s particle-wave complementarity principle, Bohm’s wave function and Bell’s theorem. In the meantime, it is suggested that the result may also serve as a resolution, rather than a falsification, to the EPR paradox and, therefore, a equilibrium-based logical unification of local realism and quantum non-locality.

References

[1] S. Blackburn, “Hume and Thick Connexions,” Philosophy and Phenomenological Research, Vol. 50, 1990, pp. 237-250. doi:10.2307/2108041

[2] L. A. Zadeh, “Causality Is Undefinable—Toward a Theory of Hierarchical Definability,” Proceedings of FUZZIEEE, Melbourne, 2-5 December 2001, pp. 67-68

[3] J. S. Bell, “On the Einstein-Podolsky-Rosen Paradox,” Physics, Vol. 1, No. 3, 1964, pp. 195-200.

[4] A. Einstein, B. Podolsky and N. Rosen, “Can QuantumMechanical Description of Physical Reality Be Considered Complete? Physical Review, Vol. 47, No. 10, 1935, pp. 777-780. doi:10.1103/PhysRev.47.777

[5] N. Bohr, “On The Notions of Causality and Complementarity,” Dialectica, Vol. 2, No. 3-4, 1948, pp. 312-319.
doi:10.1111/j.1746-8361.1948.tb00703.x

[6] K. Hess and W. Philipp, “A Possible Loophole in the Theorem of Bell,” Proceedings of the National Academy of Sciences of USA, Vol. 98, No. 25, 2001, pp. 1422414227. doi:10.1073/pnas.251524998

[7] D. Bohm, “Causality and Chance in Modern Physics,” University of Pennsylvania Press, Philadelphia, 1980.

[8] M. Kumar, “Quantum: Einstein, Bohr, and the Great Debate about the Nature of Reality,” Norton & Company, New York/London, 2010.

[9] W.-R. Zhang, “Equilibrium Relations and Bipolar Cognitive Mapping for Online Analytical Processing with Applications in International Relations and Strategic Decision Support,” IEEE Transactions on SMC, Part B, Vol. 33. No. 2, 2003, pp. 295-307.

[10] W -R. Zhang and L. Zhang, “YinYang Bipolar Logic and Bipolar Fuzzy Logic,” Information Sciences, Vol. 165, No. 3-4, 2004, pp. 265-287.
doi:10.1016/j.ins.2003.05.010

[11] W.-R. Zhang, “YinYang Bipolar Lattices and L-Sets for Bipolar Knowledge Fusion, Visualization, and Decision,” International Journal of Information Technology and Decision Making, Vol. 4, No. 4, 2005, pp. 621-645
doi:10.1142/S0219622005001763

[12] W.-R. Zhang, “YinYang Bipolar Relativity: A Unifying Theory of Nature, Agents and Causality with Applications in Quantum Computing, Cognitive Informatics and Life Sciences,” IGI Global, Hershey, 2011.

[13] L. Bombelli, J. Lee, D. Meyer and R. D. Sorkin, “Spacetime as a Causal Set,” Physical Review Letters, Vol. 59, No. 5, 1987, pp. 521-524.
doi:10.1103/PhysRevLett.59.521

[14] W.-R. Zhang, “YinYang Bipolar Atom: An Eastern Road toward Quantum Gravity,” Journal of Modern Physics, Vol. 3, 2012, pp. 1261-1271.
doi:10.4236/jmp.2012.329163

[15] W.-R. Zhang, “Beyond Spacetime Geometry: The Death of Philosophy and Its Reincarnation,” Journal of Modern Physic, Vol. 3, 2012, pp. 1272-1284.
doi:10.4236/jmp.2012.329164

[16] R. J. Yañez, A. R. Plastino and J. S. Dehesa, “Quantum Entanglement in a Soluble Two-Electron Model Atom,” The European Physical Journal D, Vol. 56, No. 1, 2010, pp. 141-150. doi:10.1140/epjd/e2009-00270-x

[17] D. Salart, A. Baas, C. Branciard, N. Gisin and Z. Hugo, “Testing the Speed of ‘Spooky Action at a Distance’,” Nature, Vol. 454, 2008, pp. 861-864.
doi:10.1038/nature07121

[18] C. H. Bennett, “Logical Reversibility of Computation,” IBM Journal of Research and Development, Vol. 17, 1973, pp. 525-532. doi:10.1147/rd.176.0525

[19] T. Toffoli, “Reversible Computing,” Tech. Memo MIT /LCS/TM-151, MIT Lab. for Com. Sci., Boston, 1980.

[20] S. Hawking and L. Mlodinow, “The Grand Design,” Random House Digital, Inc., New York, 2010.

[21] J. Gore and A. van Oudenaarden, “Synthetic Biology: The Yin and Yang of Nature,” Nature, Vol. 457, No. 7227, 2009, pp. 271-272. doi:10.1038/457271a

[22] Y. Shi, E. Seto, L.-S. Chang and T. Shenk, “Transcriptional Repression by YY1, a Human GLI-Kruppel-Related Protein, and Relief of Repression by Adenovirus E1A Protein,” Cell, Vol. 67, No. 2, 1991, pp. 377-388.
doi:10.1016/0092-8674(91)90189-6

[23] B. M. Jacobsen and D. G. Skalnik,“YY1 Binds Five cis-Elements and Trans-Activates the Myeloid Cell-Restricted gp91phox Promoter,” The Journal of Biological Chemistry, Vol. 274, 1999, pp. 29984-29993.
doi:10.1074/jbc.274.42.29984

[24] H. Liu, M. Schmidt-Supprian, Y. Shi, E. Hobeika, N. Barteneva, H. Jumaa, R. Pelanda, M. Reth, J. Skok, K. Rajewsky and Y. Shi, “Yin Yang 1 Is a Critical Regulator of B-Cell Development,” Genes & Development, Vol. 21, 2007, pp. 1179-1189. doi:10.1101/gad.1529307

[25] L. Palko, H. W. Bass, M. J. Beyrouthy and M. M. Hurt, “The Yin Yang-1 (YY1) Protein Undergoes a DNA-Replication-Associated Switch in Localization from the Cytoplasm to the Nucleus at the Onset of S Phase,” Journal of Cell Science, Vol. 117, 2004, pp. 465-476.
doi:10.1242/jcs.00870

[26] S. Vasudevan, Y. Tong and J. A. Steitz, “Switching from Repression to Activation: MicroRNAs Can Up-Regulate Translation,” Science, Vol. 318, No. 5858, 2007, pp. 19311934. doi:10.1126/science.1149460

[27] W.-R, Zhang, H. J. Zhang, Y. Shi and S. S. Chen, “Bipolar Linear Algebra and YinYang-N-Element Cellular Networks for Equilibrium-Based Biosystem Simulation and Regulation,” Journal of Biological Systems, Vol. 17, No. 4, 2009, pp. 547-576. doi:10.1142/S0218339009002958

[28] W.-R. Zhang, S. Chen and J. C. Bezdek, “A Generic System for Cognitive Map Development and Decision Analysis,” IEEE Transactions on Systems, Man, and Cybernetics, Vol. 19, No. 1, 1989, pp. 31-39.
doi:10.1109/21.24529

[29] W.-R. Zhang, S. Chen, W. Wang and R. King, “A Cognitive Map Based Approach to the Coordination of Distributed Cooperative Agents,” IEEE Transactions on Systems, Man, and Cybernetics, Vol. 22, No. 1, 1992, pp. 103-114.
doi:10.1109/21.141315

[30] Fermi National Accelerator Laboratory, Press Room 06-19, 25 September 2006.

[31] W.-R. Zhang, A. Pandurangi and K. Peace, “YinYang Dynamic Neurobiological Modeling and Diagnostic Analysis of Major Depressive and Bipolar Disorders,” IEEE Transactions on Biomedical Engineering, Vol. 54, No. 10, 2007, pp. 1729-1739. doi:10.1109/TBME.2007.894832

[32] W.-R., Zhang, K. A. Pandurangi, K. E. Peace, Y. Zhang and Z. Zhao, “MentalSquares: A Generic Bipolar Support Vector Machine for Psychiatric Disorder Classification, Diagnostic Analysis and Neurobiological Data Mining,” International Journal on Data Mining and Bioinformatics, Vol. 17, No. 4, 2011, pp. 547-576.

[33] W.-R. Zhang, “YinYang Bipolar Fuzzy Sets and Fuzzy Equilibrium Relations for Bipolar Clustering, Optimization, and Global Regulation,” International Journal of Information Technology and Decision Making, Vol. 5, No. 1, 2006, pp. 19-46.

[34] A. Einstein,”Considerations Concerning the Fundaments of Theoretical Physics,” Science, Vol. 91, No. 2369, 1940, pp. 487-491. doi:10.1126/science.91.2369.487

[35] P. Shor, “Algorithms for Quantum Computation: Discrete Log and Factoring,” Proceedings of 35th Annual Symposium on Foundation of Computer Science, IEEE Computer Society, Los Alamitos, 1994, pp. 124-134.

[36] G. Birkhoff and J. von Neumann, “The Logic of Quantum Mechanics,” Annals of Mathematics, Vol. 37, No. 4, 1936, pp. 823-843. doi:10.2307/1968621

[37] P. Woit, “Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Law,” Basic Book, New York, 2006.

[38] L. A. Zadeh, “Fuzzy Logic,” Scholarpedia, Vol. 3, No. 3, 2008, p. 1766.