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One of the most challenging open problems in quantum information theory is to clarify and quantify how entanglement behaves when part of an entangled state is sent through a quantum channel. Of central importance in the description of a…
Two quantum channels are called compatible if they can be obtained as marginals from a single broadcasting channel; otherwise they are incompatible. We derive a characterization of the compatibility relation in terms of concatenation and…
We present a new application of harmonic analysis to quantum information by constructing intriguing classes of quantum channels stemming from specific representations of multiplier algebras over locally compact groups $G$. Beginning with a…
Quantum channel, as the information transmitter, is an indispensable tool in quantum information theory. In this paper, we study a class of special quantum channels named the mixed-permutation channels. The properties of these channels are…
We study a natural generalization of the additivity problem in quantum information theory: given a pair of quantum channels, then what is the set of convex trace functions that attain their maximum on unentangled inputs, if they are applied…
In this paper we will demonstrate that any compact quantum group can be used as symmetry groups for quantum channels, which leads us to the concept of covariant channels. We, then, unearth the structure of the convex set of covariant…
We obtain an explicit characterization of linear maps, in particular, quantum channels, which are covariant with respect to an irreducible representation ($U$) of a finite group ($G$), whenever $U \otimes U^c$ is simply reducible (with…
Understanding quantum channels and the strange behavior of their capacities is a key objective of quantum information theory. Here we study a remarkably simple, low-dimensional, single-parameter family of quantum channels with exotic…
In this work we design a specific simulation tool for quantum channels which is based on the use of a control system. This allows us to simulate an average quantum channel which is expressed in terms of an ensemble of channels, even when…
This paper continues the study of stochastic maps, or channels, which break entanglement. We give a detailed description of entanglement-breaking qubit channels, and show that such maps are precisely the convex hull of those known as…
In this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi-Jamio{\l}kowski state. The second one is based on the relative entropy…
We present a method to detect properties of quantum channels, assuming that some a priori information about the form of the channel is available. The method is based on a correspondence with entanglement detection methods for multipartite…
We consider the image of some classes of bipartite quantum states under a tensor product of random quantum channels. Depending on natural assumptions that we make on the states, the eigenvalues of their outputs have new properties which we…
We introduce an infinite sequence of quantum channels for which the Holevo capacity is additive. The channel series is closely related to the quantum channels arising from universal quantum cloning machines. The additivity proof is…
We present a general model for quantum channels with memory, and show that it is sufficiently general to encompass all causal automata: any quantum process in which outputs up to some time t do not depend on inputs at times t' > t can be…
The quantum capacity of degradable quantum channels has been proven to be additive. On the other hand, there is no general rule for the behavior of quantum capacity for non-degradable quantum channels. We introduce the set of partially…
Recently there has been considerable activity on the subject of additivity of various quantum channel capacities. Here, we construct a family of channels with sharply bounded classical, hence private capacity. On the other hand, their…
Inspired by Montanaro's work, we introduce the concept of additivity rates of a quantum channel $L$, which give the first order (linear) term of the minimum output $p$-R\'enyi entropies of $L^{\otimes r}$ as functions of $r$. We lower bound…
An example is given of a qubit quantum channel which requires four inputs to maximize the Holevo capacity. The example is one of a family of channels which are related to 3-state channels. The capacity of the product channel is studied and…
A conjecture arising naturally in the investigation of additivity of classical information capacity of quantum channels states that the maximal purity of outputs from a quantum channel, as measured by the p-norm, should be multiplicative…