Detecting entanglement of quantum channels

Chaojian Li,Bang-Hai Wang,Bujiao Wu,Xiao Yuan

Figure 1. The CNOT or SWAP gate with local depolarizing noise. Given maximally entangled input states ${{\rm{\Phi }}}_{{AA}}=| {\rm{\Phi }}\rangle {\left\langle {\rm{\Phi }}\right|}_{{AA}}$ and ${{\rm{\Phi }}}_{{BB}}=| {\rm{\Phi }}\rangle {\left\langle {\rm{\Phi }}\right|}_{{BB}}$, the output state corresponds to the Choi state of the noise channel. The task is to detect the entanglement of the output state between the bipartition between ${AA}^{\prime} $ and $B^{\prime} B$.