Multipartite secure state distribution

We introduce the distribution of a secret multipartite entangled state in a real-world scenario as a quantum primitive. We show that in the presence of noisy quantum channels (and noisy control operations), any state chosen from the set of two-colorable graph states (Calderbank-Shor-Steane codewords) can be created with high fidelity while it remains unknown to all parties. This is accomplished by either blind multipartite entanglement purification, which we introduce in this paper, or by multipartite entanglement purification of enlarged states, which offers advantages over an alternative scheme based on standard channel purification and teleportation. The parties are thus provided with a secret resource of their choice for distributed secure applications.

Figure 1

Examples of two-colorable graphs which correspond to (a) GHZ state; (b) linear cluster state; (c) two-dimensional cluster state. Vertices with the same color are not connected by edges.

Figure 2

Setup for secure distribution of multipartite entangled states based on (a) channel purification (i); (b) direct purification of multipartite entangled states (ii); (c) purification of enlarged entangled states (iii).