Related papers: The output entropy of quantum channels and operati…
A Banach space $\X$ has the complete continuity property (CCP) if each bounded linear operator from $L_1$ into $\X$ is completely continuous (i.e., maps weakly convergent sequences to norm convergent sequences). The main theorem shows that…
We consider the image of some classes of bipartite quantum states under a tensor product of random quantum channels. Depending on natural assumptions that we make on the states, the eigenvalues of their outputs have new properties which we…
We illustrate the mathematical theory of entropy production in repeated quantum measurement processes developed in a previous work by studying examples of quantum instruments displaying various interesting phenomena and singularities. We…
Quantum entropy and skew information play important roles in quantum information science. They are defined by the trace of the positive operators so that the trace inequalities often have important roles to develop the mathematical theory…
The compatibility of the semiclassical quantization of area-preserving maps with some exact identities which follow from the unitarity of the quantum evolution operator is discussed. The quantum identities involve relations between traces…
The proper definition of entropy is fundamental to the relationship between statistical mechanics and thermodynamics. It also plays a major role in the recent debate about the validity of the concept of negative temperature. In this paper,…
In this paper, we consider the minimal entropy of qubit states transmitted through two uses of a noisy quantum channel, which is modeled by the action of a completely positive trace-preserving (or stochastic) map. We provide strong support…
Quantum coherence characterizes the non-classical feature of a single party system with respect to a local basis. Based on a recently introduced resource framework, coherence can be regarded as a resource and be systematically manipulated…
For a given positive operator $G$ we consider the cones of linear maps between Banach spaces of trace class operators characterized by the Stinespring-like representation with $\sqrt{G}$-bounded and $\sqrt{G}$-infinitesimal operators…
The notion of Shannon entropy is crucial for the theory of classical information. In quantum information theory, an analogous key role is played by the von Neumann entropy: quantum information processing is closely related to entropy…
We analyze quantum communication properties of phase-covariant channels depending on their degree of non-unitality. In particular, we derive analytical formulas for minimal and maximal channel fidelity on pure states and maximal output…
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…
Let $A(k)u(k)=f(k) (1)$ be an operator equation, $X$ and $Y$ are Banach spaces, $k\in\Delta\subset\C$ is a parameter, $A(k):X\to Y$ is a map, possibly nonlinear. Sufficient conditions are given for continuity of $u(k)$ with respect to $k$.…
The Renyi entropy plays an essential role in quantum information theory. We study the continuity estimation of the Renyi entropy. An inequality relating the Renyi entropy difference of two quantum states to their trace norm distance is…
A problem in quantum information theory that has received considerable attention in recent years is the question of multiplicativity of the so-called maximal output purity (MOP) of a quantum channel. This quantity is defined as the maximum…
Information theory establishes the fundamental limits on data transmission, storage, and processing. Quantum information theory unites information theoretic ideas with an accurate quantum-mechanical description of reality to give a more…
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…
Evolution of charged quantum fields under the action of constant nonuniform electric fields is studied. To this end we construct a special generating functional for density operators of the quantum fields with different initial conditions.…
The channel output entropy of a transmitted sequence is the entropy of the possible channel outputs and similarly the channel input entropy of a received sequence is the entropy of all possible transmitted sequences. The goal of this work…
Quantum physics, despite its observables being intrinsically of a probabilistic nature, does not have a quantum entropy assigned to them. We propose a quantum entropy that quantify the randomness of a pure quantum state via a conjugate pair…