Superadditivity of a reverse private capacity in quantum channels

Abstract

Unconditionally secure information sharing of private information against an eavesdropper can be achieved with a quantum key distribution (QKD) protocol. A theoretical bound on a secure key rate of a QKD protocol is known to be realized by a reverse private capacity such as with a reverse reconciliation. We show theoretically that a reverse private capacity has a property of superadditivity, with an example consisting of two quantum channels which are a pure loss channel and an 100% erasure channel. This implies that a tighter bound for a secure key rate exists than the previously known bound based on analysis of a reverse private capacity in a single channel.