Repository logo

Superadditivity of Private Information for Any Number of Uses of the Channel.

Change log


Elkouss, David 


The quantum capacity of a quantum channel is always smaller than the capacity of the channel for private communication. Both quantities are given by the infinite regularization of the coherent and the private information, respectively, which makes their evaluation very difficult. Here, we construct a family of channels for which the private and coherent information can remain strictly superadditive for unbounded number of uses, thus demonstrating that the regularization is necessary. We prove this by showing that the coherent information is strictly larger than the private information of a smaller number of uses of the channel. This implies that even though the quantum capacity is upper bounded by the private capacity, the nonregularized quantities can be interleaved.



quant-ph, quant-ph, cs.IT, math.IT

Journal Title

Phys Rev Lett

Conference Name

Journal ISSN


Volume Title



American Physical Society (APS)
European Commission (600700)
SS acknowledges the support of Sidney Sussex College and European Union under project QALGO (Grant Agreement No. 600700). DE acknowledges financial support from the European CHIST-ERA project CQC (funded partially by MINECO grant PRI-PIMCHI- 2011-1071) and from Comunidad de Madrid (grant QUITEMAD+-CM, ref. S2013/ICE-2801). This work has been partially supported by STW, QuTech and by the project HyQuNet (Grant No. TEC2012-35673), funded by Ministerio de Economia y Competitividad (MINECO), Spain. This work was made possible through the support of grant #48322 from the John Templeton Foundation.