Quantum Probability Calculator
Compute measurement probabilities, expectation values, and entropy for any single-qubit state |ψ⟩ = α|0⟩ + β|1⟩
Common Qubit States
State Input: |ψ⟩ = α|0⟩ + β|1⟩
Normalized State
|ψ⟩ = (1.0000)|0⟩ + (0.0000)|1⟩
Measurement Probabilities
P(|0⟩)100.00%
100.0%
P(|1⟩)0.00%
⟨σₓ⟩
0.0000
⟨σᵧ⟩
0.0000
⟨σ_z⟩
1.0000
Entropy S
0.0000
Bloch θ
0.00°
Bloch φ
0.00°
About Quantum Probability
In quantum computing, a qubit exists in a superposition of |0⟩ and |1⟩ states: |ψ⟩ = α|0⟩ + β|1⟩, where α and β are complex amplitudes satisfying |α|² + |β|² = 1.
The probability of measuring |0⟩ is |α|² and |1⟩ is |β|². The Bloch sphere provides a geometric representation where θ (polar) and φ (azimuthal) angles parameterize the state.
Pauli expectation values ⟨σₓ⟩, ⟨σᵧ⟩, ⟨σ_z⟩ give the Bloch vector coordinates. The von Neumann entropy S = −Σ pᵢ log₂(pᵢ) measures the uncertainty — 0 for pure basis states, 1 for maximum superposition.