Heralded channel Holevo superadditivity bounds from entanglement monogamy

We introduce a class of channels called heralded channels, which generalize the quantum erasure channel composed with an arbitrary other quantum channel. We show that monogamy of squashed entanglement limits the superadditivity of Holevo capacity of heralded channels in the regime of rare success (frequent erasure). We prove that in the limit of near-zero success probability, the classical capacity of the heralded channel converges to its Holevo information, which is equal to success probability times the single-letter Holevo information of the channel with which erasure is composed. We also show how entanglement monogamy applies to non-classicality in quantum games, and we consider how faithful monogamous entanglement measures may bound other entanglement-dependent quantities in many-party scenarios.