Quantum Proofs

Quantum Proofs — shown in full detail, with its proof: a deterministic content-address recomputable from the component's name.

all quantum science · proven in animation

6/6 proven · 4,096 shots

H|0> is an equal superposition; outcome frequencies converge to |amplitude|^2 = 1/2.

P(0) = |<0|H|0>|^2 = 1/2

In |Φ+⟩ each qubit is random (1/2) yet the two always agree: ⟨Z0 Z1⟩ = 1.

|Φ+⟩ = (|00⟩ + |11⟩)/√2 → ⟨Z0 Z1⟩ = 1

Coherent amplitudes add before squaring: bright and dark fringes, visibility 1.

I(x) = |a(e^{+id/2} + e^{-id/2})|^2 = 4a^2 cos^2(d/2)

Gates are unitary: total probability stays exactly 1 through H and the CNOT chain.

Σ_i |amp_i|^2 = 1

Measuring projects the state; an immediate second measurement repeats the outcome.

P^2 = P → repeat agreement = 1

A Gaussian packet and its momentum dual saturate the bound: σx · σp = 1/2.

σx · σp ≥ ħ/2, equality for a Gaussian

✓ proven · content-address 388212fd-4530-8f0e-8d3a-cdfb03b1886f — declared, placed, mounted, and recomputable from the component's name.

Quantum Proofs ​