The quantum music paradox

Qubit Ostinato

The familiar E–F semitone becomes an infinite quantum score. This alternating λ = −1/2 variant switches pitch with probability 3/4; the paper’s λ = 1/2 realization switches with probability 1/4. Both preserve the stepwise endpoint law of every finite prefix.

Every finite prefixtarget: νF,k = 0
current νF,k = 0
prefixready
mixing λk−1/2
prefix product1

Ready: the first Qubit Ostinato note lies on the zero set.

Each playback samples a new E–F trajectory while the quantum prefix follows the green Born target.

Qubit Ostinato infinity chain on a Bloch sphere The blue accumulated quantum prefix meets the green stochastic target latitude while the red next unitary note is selected from the zero set. xyz
quantum prefix next unitary note stochastic target
rk = (0, 0, 1) tk = (−0.866, 0, −0.500)
outcome 0 — E2outcome 1 — F2

Born-flow score — eight-note windows

Qubit Ostinato keeps playing
Eight-step Born-flow score for Qubit Ostinato Each eight-note window deposits one sampled path across eight E and F columns. U1 U2 U3 U4 U5 U6 U7 U8 E F E F

No eight-note paths yet.