The computational basis is the standard basis for quantum measurement: |0⟩ maps to outcome 0 and |1⟩ maps to outcome 1. For multiple qubits, basis states are labeled by binary strings such as |00⟩, |01⟩, |10⟩, and |11⟩. section 4.1.1
Measurement in the computational basis follows these rules:
- A qubit in α|0⟩ + β|1⟩ produces 0 with probability α² and 1 with probability β² when the amplitudes are real. section 4.1.1
- For a multiqubit superposition, each binary-string outcome has probability equal to the square of its corresponding amplitude. section 4.1.1
- A system already in a computational-basis state yields its matching binary string with probability 1. section 4.1.1
Two-qubit readout
For a state a₀|00⟩ + a₁|10⟩ + a₂|01⟩ + a₃|11⟩, measurement can return each listed binary string, with probabilities a₀², a₁², a₂², and a₃² respectively. If the state is |01⟩, the result is always 01. section 4.1.1
Figure 4.2 Measuring two qubits in a superposition of all basis states can give any of the results 00, 01, 10, and 11, with probabilities equal to squares of the amplitudes of the corresponding basis states in the superposition state. When we measure a system that is in a specific basis state, we can only get the result that corresponds to that state, with 100% probability.
Visualizes how amplitudes determine the possible computational-basis outcomes for two qubits. section 4.1.1
