Leonardo Rossetti - Universtà di Camerino

Nonmultiplicativity of the Holevo Barycenter

The Holevo barycenter of a quantum channel is the unique output state obtained as the average output of any ensemble achieving the Holevo capacity. Given two quantum channels, a natural question is whether this barycenter tensorizes under parallel composition, namely whether the barycenter of the product channel coincides with the tensor product of the individual barycenters. This question is closely related to the additivity problem for the Holevo capacity: additivity implies tensorization of the Holevo barycenter, while tensorization alone is not sufficient for additivity. Although the Shor--Hastings construction guarantees the existence of channels with non-additive Holevo capacity, the corresponding Holevo barycenters still tensorize, leaving open whether the tensorization property might hold universally. In this work, we answer this question in the negative by exhibiting a channel whose tensor square violates multiplicativity of the Holevo barycenter. Moreover, we show that the entropy of the Holevo barycenter is neither universally subadditive nor universally superadditive under tensor squaring.