Hybrid Zero-capacity Channels

There are only two known kinds of zero-capacity channels. The first kind produces entangled states that have positive partial transpose, and the second one - states that are cloneable. We consider the family of 'hybrid' quantum channels, which lies in the intersection of the above classes of channels and investigate its properties. It gives rise to the first explicit examples of the channels, which create bound entangled states that have the property of being cloneable to the arbitrary finite number of parties. Hybrid channels provide the first example of highly cloneable binding entanglement channels, for which known superactivation protocols must fail - superactivation is the effect where two channels each with zero quantum capacity having positive capacity when used together. We give two methods to construct a hybrid channel from any binding entanglement channel. We also find the low-dimensional counterparts of hybrid states - bipartite qubit states which are extendible and possess two-way key

Game-theoretic characterization of antidegradable channels

We introduce a guessing game involving a quantum channel, three parties - the sender, the receiver and an eavesdropper, Eve - and a quantum public side channel. We prove that a necessary and sufficient condition for the quantum channel to be antidegradable, is that Eve wins the game. We thus obtain a complete operational characterization of antidegradable channels in a game-theoretic framework.Comment: v2: published version, 14 pages, 1 figure; v1: 13 pages, 1 figur

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

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.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.This is the author accepted manuscript. The final version of the article is available from APS at http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.115.04050

Quantum Capacity Can Be Greater Than Private Information for Arbitrarily Many Uses

The quantum capacity of a quantum channel is always smaller than the capacity of the channel for private communication. However, both quantities are given by the infinite regularization of respectively the coherent and the private information. Here, we construct a family of channels for which the private and coherent information can remain strictly superadditive for unbounded number of uses. 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. It turns out that even though the quantum capacity is upper bounded by the private capacity, the non-regularized quantities can be interleaved. From an operational point of view, the private capacity can be used for gauging the practical value of quantum channels for secure communication and, consequently, for key distribution. We thus show that in order to evaluate the interest a channel for this task it is necessary to optimize the private information over an unlimited number of uses of the channel