Manipulate a pure qubit on a Bloch sphere while its relative phase precesses. A separate complex-amplitude compass and three-axis measurement frame connect phase to observable probabilities.
• A Bloch sphere, state vector, measurement axes, a complex-coefficient compass and two outcome columns. • Controls for polar preparation angle (°), initial relative phase (°), relative-phase precession (°/s) and measurement basis. • Four tabs: Quantum bench, Probabilities & measurements, Experiments (with built-in model checks), and Learn & assess.
|ψ⟩ = cos(θ/2)|0⟩ + e^(iφ) sin(θ/2)|1⟩, with Bloch vector r = (sinθ cosφ, sinθ sinφ, cosθ). Along any axis P(+) = (1 + r_axis)/2 and P(−) = 1 − P(+). The phase advances as φ(t) = φ0 + ωt, and the state norm² stays 1.
The model is an ideal isolated pure qubit with a prescribed relative-phase rotation. It has no decoherence, gate calibration errors or spatial particle motion, and Bloch-space geometry is not real-space geometry. Global phase is omitted because it cannot affect these measurement probabilities.
No. It represents state-space evolution, not motion through real space.
Yes. Relative phase determines the X component of the Bloch vector, so X-basis probabilities oscillate while Z-basis probabilities can stay unchanged.
For an equator state with the Z basis selected, both probabilities stay at 50% while phase advances (the "Z ignores relative phase" preset); the X positive probability instead oscillates between 0 and 100%.
It is an ideal isolated pure qubit with a prescribed phase rotation: no decoherence, gate calibration errors or spatial particle motion, and global phase is omitted.