Two-State System - Quantum States & Qubits Step by Step

A two-state system is modeled with two possible measurement outcomes and an amplitude attached to each outcome. The outcome budget is exact only for the declared basis and ideal state preparation; real qubits add leakage, decoherence, preparation error, basis misalignment, and readout uncertainty.

A qubit is a physical two-outcome system described by amplitudes. 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 qubit has two measurement outcomes

The state is written with an amplitude for outcome zero and an amplitude for outcome one.

\lvert 0\rangle,\quad \lvert 1\rangle

A basis state has probability one

This basis state has probability 1 for outcome zero.

P(\text{zero}) = 1

Each two-outcome budget sums to one

A two-state system can put the whole budget on zero, the whole budget on one, or split the budget. The probabilities still add to one.

\begin{array}{c|c|c}\text{case}&P_{\text{zero}}&P_{\text{one}}\\0&1&0\\1&0&1\\2&\frac{1}{2}&\frac{1}{2}\end{array}