Entanglement Cost of Antisymmetric States and Additivity of Capacity of Some Quantum Channel

We study the entanglement cost of the states in the contragredient space, which consists of $(d-1)$ $d$-dimensional systems. The cost is always $\log_2 (d-1)$ ebits when the state is divided into bipartite \C^d \otimes (\C^d)^{d-2}. Combined with the arguments in \cite{Matsumoto02}, additivity of channel capacity of some quantum channels is also shown.Comment: revtex 4 pages, no figures, small changes in title and author's affiliation and some typo are correcte

Fundamental Cycle of a Periodic Box-Ball System

We investigate a soliton cellular automaton (Box-Ball system) with periodic boundary conditions. Since the cellular automaton is a deterministic dynamical system that takes only a finite number of states, it will exhibit periodic motion. We determine its fundamental cycle for a given initial state.Comment: 28 pages, 6 figure

A crystal theoretic method for finding rigged configurations from paths

The Kerov--Kirillov--Reshetikhin (KKR) bijection gives one to one correspondences between the set of highest paths and the set of rigged configurations. In this paper, we give a crystal theoretic reformulation of the KKR map from the paths to rigged configurations, using the combinatorial R and energy functions. This formalism provides tool for analysis of the periodic box-ball systems.Comment: 24 pages, version for publicatio

Digital technologies in lending small and medium-size enterprises in Russia

Purpose: The article is devoted to the assessment of changes in the forms and methods of lending Russian Small and Medium-sized Enterprises (SMEs). The purpose is to outline the role of digital technologies in the system of lending SMEs in Russia. Design/Methodology/Approach: To achieve this goal it is necessary: first, to outline the main changes in the banking industry considering digital technologies, second, to list the main banking products, how digital technologies influence the most (banks as ecosystems) and third, to describe how digital technologies are beneficial in lending SMEs. Findings: The authors defined the crucial role of digital technologies, underlined the leading role of the Russian financial sector in the world according to experts and offered the scheme of a digital banking product development. Also, the authors compared digital development in the EU and in Russia and made the conclusion towards some new opportunities to SMEs. Practical Implications: The research results may be implicated in a system of lending by means of digital products offered to SMEs and future key points of development in the digital sphere for the commercial banks, e-trade and fintech companies. Originality/Value: The main contribution of this article is in comparison between digital development in the EU and Russia, some leading role of the Russian banks in the world, description of a digital banking product development and considering the experience of the ecosystem of Sberbank for SMEs in Russia.peer-reviewe

Entanglement Cost of Three-Level Antisymmetric States

We show that the entanglement cost of the three-dimensional antisymmetric states is one ebit.Comment: 8page

"Squashed Entanglement" - An Additive Entanglement Measure

In this paper, we present a new entanglement monotone for bipartite quantum states. Its definition is inspired by the so-called intrinsic information of classical cryptography and is given by the halved minimum quantum conditional mutual information over all tripartite state extensions. We derive certain properties of the new measure which we call "squashed entanglement": it is a lower bound on entanglement of formation and an upper bound on distillable entanglement. Furthermore, it is convex, additive on tensor products, and superadditive in general. Continuity in the state is the only property of our entanglement measure which we cannot provide a proof for. We present some evidence, however, that our quantity has this property, the strongest indication being a conjectured Fannes type inequality for the conditional von Neumann entropy. This inequality is proved in the classical case.Comment: 8 pages, revtex4. v2 has some more references and a bit more discussion, v3 continuity discussion extended, typos correcte

Relationships Between Two Approaches: Rigged Configurations and 10-Eliminations

There are two distinct approaches to the study of initial value problem of the periodic box-ball systems. One way is the rigged configuration approach due to Kuniba--Takagi--Takenouchi and another way is the 10-elimination approach due to Mada--Idzumi--Tokihiro. In this paper, we describe precisely interrelations between these two approaches.Comment: 16 pages, final version, minor revisio