346 research outputs found
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 -dimensional systems. The cost is always 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 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
Correlation function for a periodic box-ball system
We investigate correlation functions in a periodic box-ball system. For the
two point functions of short distance, we give explicit formulae obtained by
combinatorial methods. We give expressions for general N-point functions in
terms of ultradiscrete theta functions.Comment: 13 pages, 2 figures, submitted to J. Phys. A: Math. Theo
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
Tropical Krichever construction for the non-periodic box and ball system
A solution for an initial value problem of the box and ball system is
constructed from a solution of the periodic box and ball system. The
construction is done through a specific limiting process based on the theory of
tropical geometry. This method gives a tropical analogue of the Krichever
construction, which is an algebro-geometric method to construct exact solutions
to integrable systems, for the non-periodic system.Comment: 13 pages, 1 figur
"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
Monogamy of entanglement and other correlations
It has been observed by numerous authors that a quantum system being
entangled with another one limits its possible entanglement with a third
system: this has been dubbed the "monogamous nature of entanglement". In this
paper we present a simple identity which captures the trade-off between
entanglement and classical correlation, which can be used to derive rigorous
monogamy relations.
We also prove various other trade-offs of a monogamy nature for other
entanglement measures and secret and total correlation measures.Comment: 7 pages, revtex
- âŠ