Quantum superadditivity in linear optics networks: Sending bits via multiple-access Gaussian channels

Superadditivity effects of communication capacities are known in the case of discrete variable quantum channels. We describe the continuous variable analog of one of these effects in the framework of Gaussian multiple access channels (MACs). Classically, superadditivity-type effects are strongly restricted: For example, adding resources to one sender is never advantageous to other senders in sending their respective information to the receiver. We show that this rule can be surpassed using quantum resources, giving rise to a type of truly quantum superadditivity. This is illustrated here for two examples of experimentally feasible Gaussian MACs.

Figure 1

Two schemes for entanglement-assisted single-user classical capacity superadditivity based on (a) a beam-splitter MAC and (b) a triple quantum nondemolition sum gate MAC. The quantity of interest is the capacity attainable by the top sender.

Figure 2

Ratios of the classical capacities of entanglement-assisted channels and regularized capacities of the same channels with product inputs as functions of the power constraints for (a) the beam-splitter channel of Fig. 1a, (b) the cut for $N_1=1000$; and (c) the triple QND sum gate channel of Fig. 1b, (d) the cut for $N=100$. In (b), the bold line depicts results obtained using condition (7), while the other lines are results for exemplary beam-splitters with transmittivities of 80%, 90%, 94%, and 98%. The break-even squeezing values for these beam-splitters are $6.34$, $5.73$, $5.79$, and $7.69$ dB, respectively.