Related papers: Advanced Alicki-Fannes-Winter method for energy-co…
We describe a modification of the Alicki-Fannes-Winter method which allows to prove uniform continuity on the set of quantum states with bounded energy of any locally almost affine function having limited growth with increasing energy. Some…
We consider a quasi-classical version of the Alicki-Fannes-Winter technique widely used for quantitative continuity analysis of characteristics of quantum systems and channels. This version allows us to obtain continuity bounds under…
General methods of quantitative and qualitative continuity analysis of characteristics of composite quantum systems are described. Several modifications of the Alicki-Fannes-Winter method are considered, which make it applicable to a wide…
We describe an advanced version of the AFW-technique proposed in [Lett. Math. Phys., 113, 121 (2023)],[Lobachevskii J. Math., 44(6), 2169 (2023)] which allows us to obtain lower semicontinuity bounds, continuity bounds and local lower…
In this article, we generalize a proof technique by Alicki, Fannes and Winter and introduce a method to prove continuity bounds for entropic quantities derived from different quantum relative entropies. For the Umegaki relative entropy, we…
We present a bouquet of continuity bounds for quantum entropies, falling broadly into two classes: First, a tight analysis of the Alicki-Fannes continuity bounds for the conditional von Neumann entropy, reaching almost the best possible…
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…
We develop an approximation approach to infinite dimensional quantum channels based on detailed investigation of the continuity properties of entropic characteristics of quantum channels and operations (trace-nonincreasing completely…
Based on the proofs of the continuity of the conditional entropy by Alicki, Fannes, and Winter, we introduce in this work the almost locally affine (ALAFF) method. This method allows us to prove a great variety of continuity bounds for the…
By extending the concept of energy-constrained diamond norms, we obtain continuity bounds on the dynamics of both closed and open quantum systems in infinite-dimensions, which are stronger than previously known bounds. We extensively…
The Alicki-Lindblad-Fannes dynamical (ALF) entropy measures the rate at which new information is gathered about a quantum system by inspecting its long-time evolution. We propose an extension of the ALF entropy to open quantum dynamics as a…
Basic properties of the unified entropies are examined. The consideration is mainly restricted to the finite-dimensional quantum case. Bounds in terms of ensembles of quantum states are given. Both the continuity in Fannes' sense and…
We obtain continuity bounds for basic information characteristics of quantum channels depending on their input dimension (if it is finite) and on the input energy bound (if the input dimension is infinite). We pay a special attention to the…
We perform a systematic study of the thermodynamics of quantum gases in the unitarity limit. Our study makes use of a "Universality Hypothesis" for the relevant energy scales of a many-body system at unitarity. This Hypothesis is supported…
The maximum entropy principle, as applied to quantum systems, is a fundamental prescript positing that for a quantum system for which we only have partial knowledge, the maximum entropy state consistent with the partial knowledge is a…
We start with Fannes' type and Winter's type tight continuity bounds for the quantum conditional mutual information and their specifications for states of special types. Then we analyse continuity of the Holevo quantity with respect to…
Semiclassical theories like the Thomas-Fermi and Wigner-Kirkwood methods give a good description of the smooth average part of the total energy of a Fermi gas in some external potential when the chemical potential is varied. However, in…
A multi-particle extension of the Arnol'd Cat Hamiltonian system is defined and examined. We propose to compute its Alicki-Fannes quantum dynamical entropy, to validate (or disprove) the validity of the decoherence approach to quantum…
We give response to the question: in infinite dimension states,given a state with energy bounded by E, we can write the state as a countable convex combination of pure states with energy bounded by E. We review the Alicki-Fannes-Winter…
Several important measures of quantum correlations of a state of a finite-dimensional composite system are defined as linear combinations of marginal entropies of this state. This paper is devoted to the infinite-dimensional generalizations…