Abstract
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.
Highlights
Aristotle’s causality principle denotes a necessary relationship between one event called cause and another event called effect which is the direct consequence of the cause
It is shown that: 1) bipolar dynamic logic (BDL) leads to logically definable causality and generic particle-antiparticle bipolar quantum entanglement; 2) bipolar quantum linear algebra (BQLA) makes composite atom-atom bipolar quantum entanglement reachable
Logically definable causality for quantum entanglement remains a mystery until today and the validity of Bell inequalities is still been questioned with experimental loopholes [6]
Summary
Aristotle’s causality principle denotes a necessary relationship between one event called cause and another event called effect which is the direct consequence of the cause. Actionreaction, particle-antiparticle, input-output, negativepositive energies, or the Yin and Yang of nature in general constitute the most fundamental opposites, but man and woman, space and time, particle and wave, truth and falsity are not exactly bipolar opposites This could be the reason why Bohr believed that a causal description of a quantum process cannot be attained and quantum mechanics has to content itself with particle-wave complementary descriptions [2]. Further extending Bohr’s particle-wave complementarity principle and Bell’s theorem, this work introduces an equilibrium-based logical interpretation to quantum causality and entanglement for quantum logic gate design and quantum cellular combinatorics. The two levels of causality and entanglements enable the generalization of quantum logic gate matrix from unipolar truth-based domain to bipolar equilibriumbased domain This generalization presents a unification of digital computing, quantum computing and bio-cellular computing with a possible resolution to the EPR paradox.
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