Correlation additivity relation is superadditive for separable states

TL;DR

This paper demonstrates that the correlation additivity relation is superadditive for separable quantum states, challenging previous conjectures about correlation subadditivity in quantum information theory.

Contribution

It provides a concrete counterexample to the general correlation subadditivity conjecture and clarifies that the additivity relation is superadditive for separable states.

Findings

Counterexample to the correlation subadditivity conjecture

Correlation additivity is superadditive for separable states

Proves the conjecture's generality is limited

Abstract

We deny with a concrete example the generality of the correlation subadditivity relation conjectured by Modi et al's [Phys. Rev. Lett. {\bf 104}, 080501 (2010)] for any quantum state and point out that the correlation additivity relation is actually super-additive for separable states. This work indicates that any effort on explicitly proving the conjecture and finding the subadditivity source is unnecessary and fruitless.