Tri-state+ communication symmetry using the algebraic approach

This work uses the algebraic approach to show how we communicate when applying the quantum mechanics (QM) concept of coherence, proposing tri-state+ in quantum computing (QC). In analogy to Einstein's stimulated emission, when explaining the thermal radiation of quantum bodies in communication, this work shows that one can use the classical Information Theory by Shannon (with two, random logical states only, “0” and “1”, emulating a relay), and add a coherent third truth value Z, as a new process that breaks the Law of the Excluded Middle (LEM). Using a well-known result in topology and projection as a “new hypothesis” here, a higher dimensional state can embed in a lower-dimensional state. This means that any three-valued logic system, breaking the LEM, can be represented in a binary logical system, obeying the LEM. This satisfies QC in behavior, offering multiple states at the same time in GF(3$^{m}$), but frees the implementation to use binary logic and LEM. This promises to allow indeterminacy, such as contingency, reference failure, vagueness, majority voting, conditionals, computability, the semantic paradoxes, and many more, to play a role in logic synthesis, with a much better resolution of indeterminate contributions to obtain coherence and help cybersecurity. We establish a link between Einstein's and Shannon's theories in QM, hitherto not reported, and use it to provide a model for QC without relying on external devices (i.e., quantum annealing), or incurring in decoherence. By focusing on adequate software, this could replace the emphasis in QC, from hardware to software.