Simultaneous superadditivity of the direct and complementary channel capacities

TL;DR

This paper demonstrates that both the coherent and private information of a quantum channel and its complement can be simultaneously superadditive over multiple uses, challenging traditional views on entanglement monogamy.

Contribution

It introduces the concept of max and total private information and shows their superadditivity properties, revealing new limits of quantum channel capacities.

Findings

Coherent and private information can be simultaneously superadditive.

Max and total private information can obey different inequality sequences.

Superadditivity persists over arbitrarily many channel uses.

Abstract

Quantum communication channels differ from their classical counterparts because their capacities can be superadditive. The principle of monogamy of entanglement suggests that superadditive improvements in the transmission capacity of a channel should reduce the amount of information loss to the environment. We challenge this intuition by demonstrating that the coherent and private information of a channel and its complement can be simultaneously superadditive for arbitrarily many channel uses. To quantify the limits of this effect, we consider the notion of max (resp. total) private information of a channel, which represents the maximum (resp. sum) of the private information of the channel itself and its complement, and study its relationship with the coherent information of the individual direct and complementary channels. For a varying number of channel uses, we show that these quantities can obey different interleaving sequences of inequalities.