Quantum state tomography estimates an unknown quantum state by measuring multiple identically prepared copies and analyzing the resulting outcomes. A single measurement reveals limited information; different measurements across copies support a more accurate reconstruction. section 4.5 section 4.9
For a single-qubit state α|0⟩ + β|1⟩, tomography can estimate unknown real coefficients α and β. Because a global phase of −1 cannot be physically distinguished, the reconstruction assumes α is nonnegative. section 4.5
A practical reconstruction workflow is to:
- Prepare or obtain multiple copies of the same unknown state. section 4.5
- Apply different measurement procedures, including bases other than the computational basis when appropriate. section 4.5 section 4.9
- Analyze the outcomes to estimate the state, recognizing that accuracy depends on information collected across multiple trials. section 4.5
Single-qubit reconstruction
Given many systems in the same unknown state α|0⟩ + β|1⟩, use measurement data to estimate α and β rather than relying on one destructive observation. section 4.5
Tomography can be extended as an exploration to two-qubit or multiqubit states, and its measurement-based ideas connect to broader tasks in quantum-state analysis. section 4.8 section 4.9
