Bit-flipped Bell resource teleportation (${\rho }_{\mathrm{out}}=p\rho +(1-p)X\rho X$)

Distributing one half of $|{\Phi }^{+}⟩$ through a quantum bit-flip channel produces $p{\Pi }_{{\Phi }^{+}}+(1-p){\Pi }_{{\Psi }^{+}}$. Ideal quantum teleportation with error-free classical correction bits induces the same bit-flip map on the input: conjugating the resource error by any Pauli gate correction changes at most its sign. For a pure target the squared quantum fidelity is $p+(1-p)|⟨X⟩{|}^2$. This describes noise in resource distribution, not a perfect resource supplied by an independent channel.