Related papers: A quantum version of Wielandt's inequality
Quantum Wielandt's inequality gives an optimal upper bound on the minimal length $k$ such that length-$k$ products of elements in a generating system span $M_n(\mathbb{C})$. It is conjectured that $k$ should be of order $\mathcal{O}(n^2)$…
A new bound on quantum version of Wielandt inequality for positive (not necessarily completely positive) maps has been established. Also bounds for entanglement breaking and PPT channels are put forward which are better bound than the…
We consider energy-constrained infinite-dimensional quantum channels from a given system (satisfying a certain condition) to any other systems. We show that dealing with basic capacities of these channels we may assume (accepting…
A condition for reversibility (sufficiency) of a channel with respect to a given countable family of states with bounded rank is obtained. This condition shows that a quantum channel preserving the Holevo quantity of at least one (discrete…
We introduce potential capacities of quantum channels in an operational way and provide upper bounds for these quantities, which quantify the ultimate limit of usefulness of a channel for a given task in the best possible context.…
It is shown that the capacity of a classical-quantum channel with arbitrary (possibly mixed) states equals to the maximum of the entropy bound with respect to all apriori distributions. This completes the recent result of Hausladen, Jozsa,…
We present an upper bound for the quantum channel capacity that is both additive and convex. Our bound can be interpreted as the capacity of a channel for high-fidelity quantum communication when assisted by a family of channels that have…
We generalise some well-known graph parameters to operator systems by considering their underlying quantum channels. In particular, we introduce the quantum complexity as the dimension of the smallest co-domain Hilbert space a quantum…
In a recent paper [J. Math. Phys. 47 082303 (2006)], Quantum Energy Inequalities were used to place simple geometrical bounds on the energy densities of quantum fields in Minkowskian spacetime regions. Here, we refine this analysis for…
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…
Quantum entropy inequalities are studied. Some quantum entropy inequalities are obtained by several methods. For entanglement breaking channel, we show that the entanglement-assisted classical capacity is upper bounded by $\log d$. A…
Quantum hypothesis testing is a central task in the entire field of quantum information theory. Understanding its ultimate limits will give insight into a wide range of quantum protocols and applications, from sensing to communication.…
The optimal rate of reliable communication over a quantum channel can be enhanced by pre-shared entanglement. Whereas the enhancement may be unbounded in infinite-dimensional settings even when the input power is constrained, a…
Basing on states and channels isomorphism we point out that semidefinite programming can be used as a quick test for nonzero one-way quantum channel capacity. This can be achieved by search of symmetric extensions of states isomorphic to a…
Uniform continuity bounds on entropies are generally expressed in terms of a single distance measure between a pair of probability distributions or quantum states, typically, the total variation distance or trace distance. However, if an…
Quantum communication relies on the existence of high quality quantum channels to exchange information. In practice, however, all communication links are affected by noise from the environment. Here we investigate the ability of quantum…
Many important properties of quantum channels are quantified by means of entropic functionals. Characteristics of such a kind are closely related to different representations of a quantum channel. In the Jamio{\l}kowski-Choi representation,…
Quantitative analysis of discontinuity of basic characteristics of quantum states and channels is presented. First we consider general estimates for discontinuity jump (loss) of the von Neumann entropy for a given converging sequence of…
In this study, we generate quantum channels with random Kraus operators to typically obtain almost twirling quantum channels and quantum expanders. To prove the concentration phenomena, we use matrix Bernstein's inequality. In this way, our…
We prove that a broad array of capacities of a quantum channel are continuous. That is, two channels that are close with respect to the diamond norm have correspondingly similar communication capabilities. We first show that the classical…