|ψ⟩
Itachi Quantum Studio
|ψ⟩ = α|0⟩ + β|1⟩  •  iℏ ∂|ψ⟩/∂t = Ĥ|ψ⟩
dim(ℋ) = 2ᴺ COMPLEX AMPLITUDES | C++20 SIMD KERNEL | COHERENCE 100%
INITIALIZING HILBERT SPACE & C++20 ENGINE...

The Born Rule | Quantum Measurement Probabilities & State Collapse

Quick Technical Answer: Formulated by Max Born in 1926, the Born rule states that the probability of obtaining measurement outcome |i⟩ from a quantum state |ψ⟩ = ∑ c_i |i⟩ equals the absolute square of its complex probability amplitude: P(i) = |c_i|².
Formula / Unitary: P(i) = |\langle i | \psi \rangle|^2 = |c_i|^2, \quad \sum_i P(i) = 1
Simulate this in Itachi Quantum Studio
Inspect state amplitudes, 3D Bloch sphere vector, and OpenQASM code live.
Open Circuit Builder →

Frequently Asked Questions

What happens to the relative phase of a quantum state after measurement?

Upon measurement, the state collapses irreversibly into an eigenstate corresponding to the observed outcome, erasing all relative phase information between superposition components.

Related Topics & Quantum Guides:

Quantum SuperpositionQuantum Measurement & Reset Operations