Heralded remote preparation of an arbitrary qubit ($p_{\mathrm{success}}=1/2$)

For a target pure state $|\psi ⟩$ of a qubit, choose its orthogonal complement so thatMeasuring the sender's half of this singlet state in that basis leaves the receiver in $|\psi ⟩$ when the sender obtains $|{\psi }^{\perp }⟩$. The outcome has probability one half. One classical success flag heralds the exact preparation without conveying the target's classical description.

// Target: quantum-theory.bigb

Apply heralded remote preparation of an arbitrary qubit independently to $n$ shared singlet states. The sender reports one bit indicating whether every local outcome was successful. A positive flag certifies that the receiver's block is the desired product of $n$ pure states; its probability is $2^{-n}$. A negative flag need not identify which states failed, since the whole block can be discarded.

// Target: algebra.bigb