The State-Operator Clifford Compatibility: A Real Algebraic Framework for Quantum Information

• URL: http://arxiv.org/abs/2512.07902v1
• Date: Fri, 05 Dec 2025 22:55:31 GMT
• Title: The State-Operator Clifford Compatibility: A Real Algebraic Framework for Quantum Information
• Authors: Kagwe A. Muchane,
• Abstract summary: We introduce a real, grade-preserving framework for $N$-qubit quantum computation based on the tensor product structure $Cell_2,0(mathbbR)otimes N$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We revisit the Pauli-Clifford connection to introduce a real, grade-preserving algebraic framework for $N$-qubit quantum computation based on the tensor product structure $C\ell_{2,0}(\mathbb{R})^{\otimes N}$. In this setting the bivector $J = e_{12}$ satisfies $J^{2} = -1$ and supplies the complex structure on a minimal left ideal via right-multiplication, while Pauli operations arise as left actions of suitable Clifford elements. Adopting a canonical stabilizer mapping, the $N$-qubit computational basis state $|0\cdots 0\rangle$ is represented natively by a tensor product of real algebraic idempotents. This structural choice leads to a State-Operator Clifford Compatibility law that is stable under the geometric product for $N$ qubits and aligns symbolic Clifford multiplication with unitary evolution on the Hilbert space.

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