Quantum channel detection

We present a method to detect properties of quantum channels, assuming that some a priori information about the form of the channel is available. The method is based on a correspondence with entanglement detection methods for multipartite density matrices based on witness operators. We first illustrate the method in the case of entanglement-breaking channels and nonseparable random unitary channels and show how it can be implemented experimentally by means of local measurements. We then study the detection of nonseparable maps and show that for pairs of systems of dimension higher than two the detection operators are not the same as in the random unitary case, highlighting a richer separability structure of quantum channels with respect to quantum states. Finally we consider the set of PPT maps, developing a technique to reveal NPT maps.

Figure 1

Scheme showing the Choi-Jamiolkowski isomorphism. On the left is the map $\mathcal{M}$; on the right is the corresponding Choi state $C_{\mathcal{M}}$.

Figure 2

Scheme of the Choi-Jamiolkowski isomorphism in the case of four-partite states. The state $|\alpha \rangle$ on the right is the maximally entangled state with respect to the bipartition AB-CD.

Figure 3

Experimental scheme implementing the detection of the $cnot$ gate.

Figure 4

Experimentally feasible scheme to implement the detection of the NPT map $\mathcal{M}$.