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

On a Periodic Soliton Cellular Automaton

We propose a box and ball system with a periodic boundary condition (pBBS). The time evolution rule of the pBBS is represented as a Boolean recurrence formula, an inverse ultradiscretization of which is shown to be equivalent with the algorithm of the calculus for the 2Nth root. The relations to the pBBS of the combinatorial R matrix of ${U'}_q(A_N^{(1)})$ are also discussed.Comment: 17 pages, 5 figure

Entanglement Cost of Three-Level Antisymmetric States

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

On the initial value problem of a periodic box-ball system

We show that the initial value problem of a periodic box-ball system can be solved in an elementary way using simple combinatorial methods.Comment: 9 pages, 2 figure