Choi-Kernel Entanglement Determines When Quantum Channels Become Perfectly Excludable

Perfect exclusion of quantum states can emerge under collective measurements even when it is impossible on a single copy. We establish the corresponding finite-copy activation law for quantum channels using the Doeblin coefficient of \(n\) channel uses. For every qubit channel, the coefficient vanishes after exactly \(\lceil \ln 2/\ln(1+r^\star)\rceil\) uses, where \(r^\star\) is the largest ratio of Schmidt coefficients among vectors in the kernel of the channel's Choi operator; it remains nonzero for all \(n\) when that kernel contains no entangled vector. The two directions admit closed-form certificates: above the threshold, a loop intervention consisting of one diagonal phase gate and local unitaries; below it, a diagonal dual witness. Classical--quantum channels recover the Pusey--Barrett--Rudolph threshold, while amplitude damping recovers the exact value of the corresponding exclusion game. In arbitrary dimension, a kernel vector with Schmidt coefficients \(c\) reduces the problem to a universal correlation-matrix optimization whose threshold is \(\lceil \ln 2/\ln(1+c_{\min}/c_{\max})\rceil\). Hence every channel whose Choi kernel contains a full-Schmidt-rank vector becomes perfectly excludable after finitely many uses, with an exact formula when the kernel is one-dimensional. For qubit channels, finite-copy perfect exclusion is equivalent to divergence of the regularized Doeblin information and therefore to an infinite asymptotic retrocausal capacity, attained with zero error after finitely many uses.