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Quantum channel, as the information transmitter, is an indispensable tool in quantum information theory. In this paper, we study a class of special quantum channels named the mixed-permutation channels. The properties of these channels are…

Quantum Physics · Physics 2024-01-15 Lin Zhang , Ming-Jing Zhao

In this paper, we show that the minimal model theory does not hold in characteristic two. More precisely, we construct counter-examples to the relative abundance conjecture.

Algebraic Geometry · Mathematics 2013-12-17 Hiromu Tanaka

We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.

Analysis of PDEs · Mathematics 2023-11-21 Florian Oschmann

Necessary and sufficient conditions for approximation of a general channel by a general source are proved. For the special case in which the channel input is deterministic, which corresponds to source simulation, we prove a stronger…

Information Theory · Computer Science 2009-08-18 Yucel Altug , Aaron B. Wagner

We consider some local entropy properties of dynamical systems under the assumption of shadowing. In the first part, we give necessary and sufficient conditions for shadowable points to be certain entropy points. In the second part, we give…

Dynamical Systems · Mathematics 2023-09-26 Noriaki Kawaguchi

This is an analysis of the additivity of the entropy of thermodynamical systems with finite heat baths. It is presented an expression for the physical entropy of weakly interacting ergodic systems, and it is shown that it is valid for both…

Statistical Mechanics · Physics 2007-05-23 M. P. Almeida

Communication rates over quantum channels can be boosted by entanglement, via superadditivity phenomena or entanglement assistance. Superadditivity refers to the capacity improvement from entangling inputs across multiple channel uses.…

Quantum Physics · Physics 2022-03-14 Haowei Shi , Quntao Zhuang

We consider the Hastings--Levitov HL(0) model in the small particle scaling limit and prove a large deviation principle. The rate function is given by the relative entropy of the driving measure $\rho$ for the Loewner--Kufarev equation: \[…

Probability · Mathematics 2025-12-03 Nathanaël Berestycki , Vladislav Guskov , Fredrik Viklund

The present work continues investigation of the capacities of measurement (quantum-classical) channels in the most general setting, initiated in~\cite{HCT}. The proof of coding theorems is given for the classical capacity and…

Quantum Physics · Physics 2014-08-15 A. A. Kuznetsova , A. S. Holevo

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…

Quantum Physics · Physics 2021-09-28 M. E. Shirokov

We prove lower bounds for the entanglement of formation and the squashed entanglement for any a bipartite density matrix in terms of the conditional entropy of the bipartite state with respect to either of its partial traces, and prove that…

Quantum Physics · Physics 2015-06-04 Eric A. Carlen , Elliott H. Lieb

In this paper, we introduce the framework for quantifying the imaginarity of quantum channels. Besides, an alternative framework is given together to simplify the process of verifying the condition. We present three imaginarity measures of…

Quantum Physics · Physics 2025-02-25 Xiangyu Chen , Qiang Lei

Quantum communication channels differ from their classical counterparts because their capacities can be superadditive. The principle of monogamy of entanglement suggests that superadditive improvements in the transmission capacity of a…

Quantum Physics · Physics 2025-11-06 Satvik Singh , Sergii Strelchuk

The super-additivity of quantum channel capacity is an important feature of quantum information theory different from classical theory, which has been attracting attention. Recently a special channel called ``platypus channel'' exhibits…

Quantum Physics · Physics 2025-06-02 Zhen Wu , Qi Zhao , Zhihao Ma

In this work we investigate the behavior of the minimal rate needed in order to guarantee a given probability that the distortion exceeds a prescribed threshold, at some fixed finite quantization block length. We show that the excess coding…

Information Theory · Computer Science 2011-02-15 Amir Ingber , Yuval Kochman

In this article we prove a non-vanishing statement, as well as several properties of metrics with minimal singularities of adjoint bundles. Our arguments involve many ideas from Y.-T. Siu's analytic proof of the finite generation of the…

Complex Variables · Mathematics 2008-07-22 Mihai Paun

A minimal counterexample to the Erd\H{o}s-Gy\'arf\'as conjecture is a graph of minimum possible order and size with minimum degree at least 3 that contains no cycle whose length is a power of 2. Markstr\"om observed that any such graph must…

Combinatorics · Mathematics 2026-05-25 Avery Carr

A coding theorem and converse are proved for a large class of abstract stationary channels with time structure including the result by Kadota and Wyner (1972) on continuous-time real-valued channels as special cases. As main contribution…

Information Theory · Computer Science 2018-04-18 Martin Mittelbach , Eduard A. Jorswieck

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…

Quantum Physics · Physics 2026-03-18 Ke Li , Quanhua Xu

The proof of additivity of entanglement of formation for some special cases is given. The strong concavity of von Neumann entropy due to strong subadditivity of von Neumann entropy is presented. Some general relations concerning about the…

Quantum Physics · Physics 2007-05-23 Heng Fan