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An Holistic Extension for Classical Logic via Quantum Fredkin Gate.

Hector Freytes1,2, Giuseppe Sergioli2

  • 1Department of Mathematics, University of Cagliari, Via Ospedale 72, I-09124 Cagliari, Italy.

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This study introduces a novel holistic extension to classical propositional logic using quantum computation principles. It explores an enhanced concept of contradiction within this quantum framework, particularly with mixed states.

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Area of Science:

  • Quantum Information Science
  • Quantum Computation
  • Quantum Logic

Background:

  • Classical propositional logic faces limitations in fully capturing complex quantum phenomena.
  • Quantum computation offers a novel framework for exploring logical extensions.
  • Mixed quantum states present unique challenges and opportunities for logical formalisms.

Purpose of the Study:

  • To introduce a holistic extension of classical propositional logic within quantum computation.
  • To investigate the application of the quantum Fredkin gate to non-factorizable bipartite states.
  • To explore an extended notion of classical contradiction in this quantum-logical framework.

Main Methods:

  • Development of a holistic logical framework based on quantum computational principles.
  • Application of the quantum Fredkin gate to non-factorizable bipartite quantum states.
  • Analysis of logical properties, including contradiction, within the extended framework.

Main Results:

  • A novel holistic extension for classical propositional logic is successfully formulated.
  • The quantum Fredkin gate is shown to be instrumental in this logical extension.
  • An extended definition of classical contradiction is established within the quantum computational context.

Conclusions:

  • The proposed holistic extension provides a richer logical framework for quantum computation.
  • Quantum gates and non-factorizable states are key components for advancing quantum logic.
  • This work opens new avenues for studying logical paradoxes in quantum systems.