Unconstrained Capacities of Quantum Key Distribution and Entanglement Distillation for Pure-Loss Bosonic Broadcast Channels

We consider quantum key distribution (QKD) and entanglement distribution using a single-sender multiple-receiver pure-loss bosonic broadcast channel. We determine the unconstrained capacity region for the distillation of bipartite entanglement and secret key between the sender and each receiver, whenever they are allowed arbitrary public classical communication. A practical implication of our result is that the capacity region demonstrated drastically improves upon rates achievable using a naive time-sharing strategy, which has been employed in previously demonstrated network QKD systems. We show a simple example of a broadcast QKD protocol overcoming the limit of the point-to-point strategy. Our result is thus an important step toward opening a new framework of network channel-based quantum communication technology.

Figure 1

(a) Single-sender $m$-receiver pure-loss linear optics quantum broadcast channel. $U^{\mathcal{L}}$ is a unitary operator of an arbitrary linear optics circuit. (b),(c) Reductions to an equivalent channel.

Figure 2

Comparison of the LOCC-assisted capacity (solid line) and the time sharing of the point-to-point capacity (dashed line). (a) Capacity region for the 1-to-2 QBC with $({\eta }_B,{\eta }_C)=(0.3,0.3)$. (b) Rate sum comparison for the 1-to-$m$ QBC with $\eta =0.1$.

Figure 3

Secret key rate region of the GC09 based CVQKD in a 1-to-2 pure-loss bosonic QBC, with $({\eta }_B,{\eta }_C)=(0.3,0.3)$. The squeezing parameter is $v=40$ (see Supplemental Material 3 [41]). The BC-CVQKD (solid line), simultaneous application of point-to-point protocol (dashed line), and time sharing of the point-to-point protocol (dotted line).