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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

$B^{\prime} B$ .