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Quantum Uncertainties and Holism Seem to Render Irrelevant Qudit-Semantics.
1Department of Economics, University of Bergamo, Via dei Caniana, 2, I-24127 Bergamo, Italy.
Entropy (Basel, Switzerland)
|July 2, 2021
Summary
This study introduces Łukasiewicz quantum computational logic, utilizing quantum circuits for a whole-to-part semantic approach. This novel quantum logic, based on qubit and qudit semantics, exhibits unique properties distinct from classical and standard quantum logic.
Area of Science:
- Quantum Information Science
- Quantum Logic
- Theoretical Computer Science
Background:
- Traditional semantics often follow a part-to-whole compositionality principle.
- Quantum mechanics exhibits holistic features that challenge standard logical frameworks.
- Existing quantum logic systems (e.g., Birkhoff-von Neumann) have limitations.
Purpose of the Study:
- To develop a novel quantum logic based on holistic quantum formalism features.
- To introduce 'Łukasiewicz quantum computational logic' with a unique semantic approach.
- To compare qubit-semantics and qudit-semantics within this new logical framework.
Main Methods:
- A semantics is defined based on holistic quantum formalism.
- Quantum circuits are employed to transform density operators from formulas to subformulas reversibly.
- A whole-to-parts procedure is utilized, contrasting with traditional compositionality.
Main Results:
- The proposed method generates a new form of quantum logic: Łukasiewicz quantum computational logic.
- Comparison reveals qubit-semantics is not stronger than the corresponding fragment of qudit-semantics, contrary to expectations.
- The developed logic is found to be weaker than classical and standard quantum logic, violating many common logical arguments.
Conclusions:
- Łukasiewicz quantum computational logic offers a distinct semantic framework for quantum computation.
- The whole-to-parts semantic approach provides a unique perspective on quantum information processing.
- The counterintuitive strength comparison between qubit and qudit semantics highlights the novelty of this quantum logic.