Not a Hidden Classical Row - Quantum States & Qubits Step by Step

A same-basis count table is not enough; the amplitude table carries the non-product state claim. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

One measurement basis can look classical

If you only measure this one basis, the same-bit counts can look like a classical list that randomly chose zero-zero or one-one.

\begin{array}{c|c}\text{outcome}&P\\\lvert 0,0\rangle&\frac{1}{2}\\\lvert 1,1\rangle&\frac{1}{2}\end{array}

The amplitude table contains a state-level test

For this two-by-two amplitude table, the product-state determinant is one half, not zero. That is a state claim, not a hidden-row caption.

\det = \frac{1}{2}\ne 0

The honest claim is correlation plus non-product state

This first book stops at exact finite-state evidence: same-basis correlation and a nonzero determinant. Later books add phase bases, hardware readout, and error budgets.

\text{same-basis correlation} + \det\ne 0