Controlled quantum teleportation in the presence of an adversary

We present a device-independent analysis of controlled quantum teleportation where the receiver is not trusted. We show that the notion of genuine tripartite nonlocality allows us to certify control power in such a scenario. By considering a specific adversarial attack strategy on a device characterized by depolarizing noise, we find that control power is a monotonically increasing function of genuine tripartite nonlocality. These results are relevant for building practical quantum communication networks and also shed light on the role of nonlocality in multipartite quantum information processing.

Figure 1

DAG representation of the causal model where $\mathrm{\Lambda }$ is the common source of correlations supplied by Derek. In a classical model, $\mathrm{\Lambda }$ is a shared random variable, whereas in a quantum model, $\mathrm{\Lambda }$ is a potentially entangled quantum state $\rho$. Here J, K, L denote the inputs of Alice, Bob, and Charlie, respectively. A, B, C denote the outcomes of Alice, Bob, and Charlie, respectively. Note that since Bob is untrusted, he can correlate his inputs with that of the common source of correlations.

Figure 2

DAG equivalence.

Figure 3

DAG for the device-independent test scenario of fully trusted controlled quantum teleportation. Note that there are no arrows from $\mathrm{\Lambda }$ to $K$, unlike the scenario of untrusted receiver considered earlier. Here, all parties have measurement choice independence and there is no communication between each other.

Figure 4

$P_{\mathrm{eff}}$, average fidelity of teleportation with controller's permission ($F_C^{NE}$), and average fidelity of teleportation without controller's permission but with eavesdropper's participation ($F_{NC}^E$) as a function of maximum Svetlichny inequality violation ($S$) given by Eq. (34) for both the qubit depolarized and total depolarized GHZ states with parameter $p\in (0,1)$.