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quant-ph2025
An Error Correctable Implication Algebra for a System of Qubits
Morrison Turnansky
We present the Lukasiewicz logic as a viable system for an implication algebra on a system of qubits. Our results show that the three valued Lukasiewicz logic can be embedded in th…
quant-ph2023
Generalizing Pauli Spin Matrices Using Cubic Lattices
Morrison Turnansky
In quantum mechanics, the connection between the operator algebraic realization and the logical models of measurement of state observables has long been an open question. In the ap…
quant-ph2023
Critical Multi-Cubic Lattices: A Novel Implication Algebra for Infinite Systems of Qudit Gates
Morrison Turnansky
We introduce a new structure, the critical multi-cubic lattice. Notably the critical multi-cubic lattice is the first true generalization of the cubic lattice to higher dimensional…