Related papers: Extending additivity from symmetric to asymmetric …
We introduce an axiomatic approach for channel divergences and channel relative entropies that is based on three information-theoretic axioms of monotonicity under superchannels (i.e. generalized data processing inequality), additivity…
We prove additivity violation of minimum output entropy of quantum channels by straightforward application of \epsilon-net argument and L\'evy's lemma. The additivity conjecture was disproved initially by Hastings. Later, a proof via…
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…
The channel capacity for the binary symmetric channel is investigated based on the symmetrized definition of the mutual information, which is arising from an attempt of extension of information content based on the nonadditivity. The…
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…
The information carrying capacity of the d-dimensional depolarizing channel is computed. It is shown that this capacity can be achieved by encoding messages as products of pure states belonging to an orthonormal basis of the state space,…
We give an elementary self-contained proof that the minimal entropy output of arbitrary products of channels $\rho \mapsto \frac{1}{d-1}(1-\rho^T)$ is additive.
Evaluating the channel capacity is one of many key problems in information theory. In this work we derive rather-mild sufficient conditions under which the capacity is finite and achievable. These conditions are derived for generic,…
It is shown that given two copies of a q-ary input channel $W$, where q is prime, it is possible to create two channels $W^-$ and $W^+$ whose symmetric capacities satisfy $I(W^-)\le I(W)\le I(W^+)$, where the inequalities are strict except…
We introduce a condition for memoryless quantum channels which, when satisfied guarantees the multiplicativity of the maximal l_p-norm with p a fixed integer. By applying the condition to qubit channels, it can be shown that it is not a…
We give a simple and conceptual proof of the fact that random unitary channels yield violation of the Minimum Output Entropy additivity. The proof relies on strong convergence of random unitary matrices and Haagerup's inequality.
Multilinear $L^p$ extrapolation results are established in a limited-range, multilinear, and off-diagonal setting for mixed-norm Lebesgue spaces over $\sigma$-finite measure spaces. Integrability exponents are allowed in the full range…
We study the multiplicativity of the output 2-norm for depolarized Werner-Holevo channels and show that multiplicativity holds for a product of two identical channels in this class. Moreover, it shown that the depolarized Werner-Holevo…
We explore complementarity between output and environment of a quantum channel (or, more generally, CP map), making an observation that the output purity characteristics for complementary CP maps coincide. Hence, validity of the…
In this paper we give several equivalent formulations of the additivity conjecture for constrained channels, which formally is substantially stronger than the unconstrained additivity. To this end a characteristic property of the optimal…
We study the convergence of states under continuous-time depolarizing channels with full rank fixed points in terms of the relative entropy. The optimal exponent of an upper bound on the relative entropy in this case is given by the…
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…
This paper investigates achievable information rates and error exponents of mismatched decoding when the channel belongs to the class of channels that are close to the decoding metric in terms of relative entropy. For both discrete- and…
In this paper we present a class of maps for which the multiplicativity of the maximal output p-norm holds when p is 2 and p is larger than or equal to 4. The class includes all positive trace-preserving maps from the matrix algebra on the…
We obtain two new additivity results of quantum channels. The first one is the additivity of the channel R\'enyi information associated with the sandwiched R\'enyi divergence of order $\alpha\in[\frac{1}{2},1)$. To prove this, we introduce…