Coupling Output Entangles - Quantum Mechanics: Waves, Spin, and Tunneling Step by Step

Treat the coupling as a checked output table, not a full hardware simulation. The toy joint state populates only zero-zero and one-one cells, and the nonzero determinant 1/2 flags that the two qubits are not independent; real coupling checks require pulse calibration, crosstalk control, decoherence budgets, readout errors, and uncertainty.

A controlled interaction is represented here only by a checked joint-state output. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A coupling output can be a joint state

The coupling lesson starts from a checked joint-state output: zero-zero and one-one carry the probability. It does not claim a hardware Hamiltonian or simulate the control pulse.

\text{coupling output is a joint table}

The joint output has two populated cells

The coupling output is summarized by the same populated diagonal cells and the nonzero determinant.

\begin{array}{c|c|c}\text{row}&\text{value}&\text{claim}\\\text{zero-zero}&\frac{1}{2}&\text{populated}\\\text{one-one}&\frac{1}{2}&\text{populated}\\\det&\frac{1}{2}&\text{not product}\\\end{array}

The joint state is not a product

The determinant is 1/2, so the state is not factored into two independent qubits.

\det=\frac{1}{2}