Related papers: Generalizing Pauli Spin Matrices Using Cubic Lattices

Generalizing Pauli Spin Matrices Using Cubic Lattices

URL: http://arxiv.org/abs/2306.05903v1
Date: Fri, 9 Jun 2023 13:54:23 GMT
Title: Generalizing Pauli Spin Matrices Using Cubic Lattices
Authors: Morrison Turnansky
Abstract summary: We show that the cubic lattice may be faithfully realized as a subset of the self-adjoint space of a von Neumann algebra. We re-derive the classic quantum gates and gain a description of how they govern a system of qubits of arbitrary cardinality.
Score: 0.0
License: http://creativecommons.org/licenses/by-nc-sa/4.0/
Abstract: 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 approach that is presented here, we introduce a new application of the cubic lattice. We claim that the cubic lattice may be faithfully realized as a subset of the self-adjoint space of a von Neumann algebra. Furthermore, we obtain a unitary representation of the symmetry group of the cubic lattice. In so doing, we re-derive the classic quantum gates and gain a description of how they govern a system of qubits of arbitrary cardinality.

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