Determinant Audits Entanglement - Quantum Computing Physical Bases: Control, Coupling, and Error Signals Step by Step

The non-product claim is the determinant check, not a caption. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The determinant is the entanglement audit

The determinant is 1/2, not 0. That is the non-product claim.

\det=\frac{1}{2}\neq0

The determinant scan crosses the product boundary

A zero determinant row is product; the checked coupled row is nonzero and must be flagged non-product.

\begin{array}{c|c|c}\text{row}&\det&\text{flag}\\\text{uncoupled}&0&\text{product}\\\text{coupled}&\frac{1}{2}&\text{not product}\\\text{audit}&\frac{1}{2}&\text{not product}\\\end{array}

The flag must match the determinant

A raw diagram cannot set the non-product flag false while keeping this determinant.

\text{notProduct}\iff \det\neq0