Related papers: Notes on entropic characteristics of quantum chann…
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,…
We consider properties of quantum channels with use of unified entropies. Extremal unravelings of quantum channel with respect to these entropies are examined. The concept of map entropy is extended in terms of the unified entropies. The…
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…
One of the major achievements of the recently emerged quantum information theory is the introduction and thorough investigation of the notion of quantum channel which is a basic building block of any data-transmitting or data-processing…
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…
Fundamental limits on communication rates over quantum channels are given by mathematical expressions involving entropic formulas. Often, it is unclear if these expressions are computable. This thesis describes contributions to the study of…
Entropic quantifiers of states lie at the cornerstone of the quantum information theory. While a quantum state can be abstracted as a device that only has outputs, the most general quantum device is a quantum channel that also has inputs.…
In analogy with its classical counterpart, a noisy quantum channel is characterized by a loss, a quantity that depends on the channel input and the quantum operation performed by the channel. The loss reflects the transmission quality: if…
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…
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…
Quantum channels, also called quantum operations, are linear, trace preserving and completely positive transformations in the space of quantum states. Such operations describe discrete time evolution of an open quantum system interacting…
Using the graphical calculus and integration techniques introduced by the authors, we study the statistical properties of outputs of products of random quantum channels for entangled inputs. In particular, we revisit and generalize models…
Spectral properties of an arbitrary matrix can be characterized by the entropy of its rescaled singular values. Any quantum operation can be described by the associated dynamical matrix or by the corresponding superoperator. The entropy of…
The von Neumann entropy of a quantum state is a central concept in physics and information theory, having a number of compelling physical interpretations. There is a certain perspective that the most fundamental notion in quantum mechanics…
When can noiseless quantum information be sent across noisy quantum devices? And at what maximum rate? These questions lie at the heart of quantum technology, but remain unanswered because of non-additivity -- a fundamental synergy which…
In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves…
Capacities of quantum channels are fundamental quantities in the theory of quantum information. A desirable property is the additivity for a capacity. However, this cannot be achieved for a few quantities that have been established as…
The entropy of a quantum operation, defined as the von Neumann entropy of the corresponding Choi-Jamio{\l}kowski state, characterizes the coupling of the principal system with the environment. For any quantum channel $\Phi$ acting on a…
Noisy quantum channels may be used in many information carrying applications. We show that different applications may result in different channel capacities. Upper bounds on several of these capacities are proved. These bounds are based on…
The operational structure of quantum couplings and entanglements is studied and classified for semifinite von Neumann algebras. We show that the classical-quantum correspondences such as quantum encodings can be treated as diagonal…