Publications

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

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 $\mathcal{C}\ell_{2,0}(\mathbb{R})^{\otimes N}$. 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 $\ket{0\cdots 0}$ 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.