Related papers: On Weyl channels being covariant with respect to t…
Some new examples of quantum channels for which the infimum of the output entropy is additive under taking a tensor product of channels are given.
We investigate decoherence induced by a quantum channel in terms of minimal output entropy and of map entropy. The latter is the von Neumann entropy of the Jamiolkowski state of the channel. Both quantities admit q-Renyi versions. We prove…
Formalism of discrete noncommutative Fourier transform is developed and applied to the study of Weyl-covariant channels. We then extend a result in quant-ph/0509126 concerning a bound of the maximal output 2-norm of a Weyl-covariant…
Quantum channels, a subset of quantum maps, describe the unitary and non-unitary evolution of quantum systems. We study a generalization of the concept of Pauli maps to the case of multipartite high dimensional quantum systems through the…
We define and study the properties of channels which are analogous to unital qubit channels in several ways. A full treatment can be given only when the dimension d is a prime power, in which case each of the (d+1) mutually unbiased bases…
We consider bistochastic quantum channels generated by unitary representations of the discret group. The proof of the additivity conjecture for the quantum depolarizing channel $\Phi$ based on the decreasing property of the relative entropy…
The additivity of minimal output entropy is proved for the Weyl channel obtained by the deformation of a q-c Weyl channel. The classical capacity of channel is calculated.
We study the four well-known capacities of a two-parameter family of qubit Pauli channels. These are the channels which are covariant under the SO(2) group and contain the depolarizing channel as a special case. We find exact expressions…
We investigate minimum output (R\'enyi) entropy of qubit channels and unital quantum channels. We obtain an exact formula for the minimum output entropy of qubit channels, and bounds for unital quantum channels. Interestingly, our bounds…
In this paper we find, for a class of bipartite quantum states, a nontrivial lower bound on the entropy gain resulting from the action of a tensor product of identity channel with an arbitrary channel. By means of that we then estimate…
Evaluating the quantum capacity of quantum channels is an important but difficult problem, even for channels of low input and output dimension. Smith and Smolin showed that the quantum capacity of the Clifford-twirl of a qubit amplitude…
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 argue that a fundamental (conjectured) property of memoryless quantum channels, namely the strong superadditivity, is intimately related to the decreasing property of the quantum relative entropy. Using the latter we first give, for a…
We introduce a class of linear maps irreducibly covariant with respect to the finite group generated by the Weyl operators. This group provides a direct generalization of the quaternion group. In particular, we analyze the irreducibly…
We consider generalizations of depolarizing channels to maps in which the identity channel is replaced by a convex combinations of unitary conjugations. We show that one can construct unital channels of this type for which the input which…
We obtained the estimation from below for the output entropy of a tensor product of the quantum phase-damping channel with an arbitrary channel. It is shown that from this estimation immediately follows that the strong superadditivity of…
We study mixed unitary channels generated by finite subgroups of the group of all unitary operators in a Hilbert space. Based on the majorization theory we introduce techniques allowing to calculate different characteristics of output…
We study quantum channels with respect to their image, i.e., the image of the set of density operators under the action of the channel. We first characterize the set of quantum channels having polytopic images and show that additivity of…
Given a quantum channel $\Phi $ in a Hilbert space $H$ put $\hat H_{\Phi}(\rho)=\min \limits_{\rho_{av}=\rho}\Sigma_{j=1}^{k}\pi_{j}S(\Phi (\rho_{j}))$, where $\rho_{av}=\Sigma_{j=1}^{k}\pi_{j}\rho_{j}$, the minimum is taken over all…
We present a complete characterization of diagonal unitary covariant (DU-covariant) superchannels, i.e. higher-order transformations transforming quantum channels into themselves. Necessary and sufficient conditions for complete positivity…