Related papers: On strong superadditivity for a class of quantum c…
We consider the depolarizing channel in $d$ dimension defined as $D_x(\rho)=(1-x)\rho+x\: \textit{tr}({\rho}) \frac{I}{d}$, and explicitly find a quantum channel ${\cal N}_x$ which anti-degrades this, when $x\geq\frac{1}{2}$. This proves…
We prove a lemma which allows one to extend results about the additivity of the minimal output entropy from highly symmetric channels to a much larger class. A similar result holds for the maximal output $p$-norm. Examples are given showing…
We address the problem of optimally approximating the action of a desired and unavailable quantum channel $\Phi $ having at our disposal a single use of a given set of other channels $\{\Psi_i \}$. The problem is recast to look for the…
Additivity of minimal entropy output is proven for the class of quantum channels $\Lambda_t (A):=t A^{T}+(1-t)\tau (A)$ in the parameter range $-2/(d^2-2)\le t \le 1/(d+1)$.
Quantum channel capacity is a fundamental quantity in order to understand how good can quantum information be transmitted or corrected when subjected to noise. However, it is generally not known how to compute such quantities, since the…
The qubit depolarizing channel with noise parameter $\eta$ transmits an input qubit perfectly with probability $1-\eta$, and outputs the completely mixed state with probability $\eta$. We show that its complementary channel has positive…
Hastings recently reported a randomized construction of channels violating the minimum output entropy additivity conjecture. Here we revisit his argument, presenting a simplified proof. In particular, we do not resort to the exact…
The continuity properties of the convex closure of the output entropy of infinite dimensional channels and their applications to the additivity problem are considered. The main result of this paper is the statement that the superadditivity…
We introduce a model of non-Gaussian quantum channel that stems from the combination of two physically relevant processes occurring in open quantum systems, namely amplitude damping and dephasing. For it we find input states approaching…
In this paper we investigate the inequality $S_q(\rho_{123})+S_q(\rho_2)\leq S_q(\rho_{12})+S_q(\rho_{23}) \, (*)$ where $\rho_{123}$ is a state on a finite dimensional Hilbert space $\mathcal{H}_1\otimes \mathcal{H}_2\otimes…
The super-additivity of quantum channel capacity is an important feature of quantum information theory different from classical theory, which has been attracting attention. Recently a special channel called ``platypus channel'' exhibits…
We study subadditivity of the minimum output entropy ($H_{min}$) of quantum multiple access channels (MACs). We provide an example of violation of the additivity theorem for $H_{min}$ known in classical information theory. Our result is…
A lower bound on the probability of decoding error of quantum communication channel is presented. The strong converse to the quantum channel coding theorem is shown immediately from the lower bound. It is the same as Arimoto's method exept…
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 investigate the structural and dynamical properties of a class of quantum channels on von Neumann algebras induced by averaging over operator groups via the Pettis integral. Utilizing the classical Yosida--Hewitt decomposition, we focus…
We describe the class (semigroup) of quantum channels mapping states with finite entropy into states with finite entropy. We show, in particular, that this class is naturally decomposed into three convex subclasses, two of them are closed…
Based on the resource theory for quantifying the coherence of quantum channels, we introduce a new coherence quantifier for quantum channels via maximum relative entropy. We prove that the maximum relative entropy for coherence of quantum…
The class of quantum states known as Werner states have several interesting properties, which often serve to illuminate unusual properties of quantum information. Closely related to these states are the Holevo-Werner channels whose Choi…
Additivity of the minimal output entropy for the family of transpose depolarizing channels introduced by Fannes et al. [quant-ph/0410195] is considered. It is shown that using the method of our previous paper [quant-ph/0403072] allows us to…
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…