Quasiparticle excitations and hierarchies of 4-dimensional quantum Hall fluid states in the matrix models

We investigate the condensate mechanism of the low-lying excitations in the matrix models of 4-dimensional quantum Hall fluids recently proposed by us. It is shown that there exist some hierarchies of 4-dimensional quantum Hall fluid states in the matrix models, and they are similar to the Haldane's hierarchy in the 2-dimensional quantum Hall fluids. However, these hierarchical fluid states appear consistently in our matrix models without any requirement of modifications of the matrix models.Comment: 5 pages, no figure, revte

Quantum Measured Information

A framework for a quantum information theory is introduced that is based on the measure of quantum information associated with probability distribution predicted by quantum measuring of state. The entanglement between states of measured system and "pointer" states of measuring apparatus, which is generated by dynamical process of quantum measurement, plays a dominant role in expressing quantum characteristics of information theory. The quantum mutual information of transmission and reception of quantum states along a noisy quantum channel is given by the change of quantum measured information. In our approach, it is not necessary to purify the transmitted state by means of the reference system. It is also clarified that there exist relations between the approach given in this letter and those given by other authors.Comment: 4 pages, revtex file, no figur

Rigid open membrane and non-abelian non-commutative Chern-Simons theory

In the Berkooz-Douglas matrix model of M theory in the presence of longitudinal $M5$-brane, we investigate the effective dynamics of the system by considering the longitudinal $M5$-brane as the background and the spherical $M5$-brane related with the other space dimensions as the probe brane. Due to there exists the background field strength provided by the source of the longitudinal $M5$-brane, an open membrane should be ended on the spherical $M5$-brane based on the topological reason. The formation of the bound brane configuration for the open membrane ending on the 5-branes in the background of longitudinal 5-brane can be used to model the 4-dimensional quantum Hall system proposed recently by Zhang and Hu. The description of the excitations of the quantum Hall soliton brane configuration is established by investigating the fluctuations of $D0$-branes living on the bound brane around their classical solution derived by the transformations of area preserving diffeomorphisms of the open membrane. We find that this effective field theory for the fluctuations is an SO(4) non-commutative Chern-Simons field theory. The matrix regularized version of this effective field theory is given in order to allow the finite $D0$-branes to live on the bound brane. We also discuss some possible applications of our results to the related topics in M-theory and to the 4-dimensional quantum Hall system.Comment: 23 pages, no figure

Rank three bipartite entangled states are distillable

We prove that the bipartite entangled state of rank three is distillable. So there is no rank three bipartite bound entangled state. By using this fact, We present some families of rank four states that are distillable. We also analyze the relation between the low rank state and the Werner state.Comment: 5 pages; no figur

Multiqubit entanglement witness

We introduce a feasible method of constructing the entanglement witness that detects the genuine entanglement of a given pure multiqubit state. We illustrate our method in the scenario of constructing the witnesses for the multiqubit states that are broadly theoretically and experimentally investigated. It is shown that our method can construct the effective witnesses for experiments. We also investigate the entanglement detection of symmetric states and mixed states.Comment: Revtex, 11 page

Entanglement of formation from optimal decomposition

We present a new method of analytically deriving the entanglement of formation of the bipartite mixed state. The method realizes the optimal decomposition families of states. Our method can lead to many new results concerning entanglement of formation, its additivity and entanglement cost. We illustrate it by investigating the two-qubit state, the separable state, the maximally correlated state, the isotropic state and the Werner state.Comment: 4 pages; Revtex; the submitted versio

Remote state preparation using non-maximally entangled states

We present a scheme in which any pure qubit |\phi=\cos{\theta}|0+\sin{\theta}e^{i\varp hi}|1 could be remotely prepared by using minimum classical bits and the previously shared non-maximally entangled states, on condition that the receiver holds the knowledge of $\theta$. Several methods are available to check the trade-off between the necessary entanglement resource and the achievable fidelity.Comment: Revtex, 8 pages, 4 figure

Distinguishing maximally entangled states locally

We demonstrate that one maximally entangled state is sufficient and necessary to distinguish a complete basis of maximally entangled states by local operation and classical communication.Comment: 1.3 pages, revtex

Optimizing classical communication in remote preparation of a general pure qubit

How to uses shared entanglement and forward classical communication to remotely prepare an arbitrary (mixed or pure) state has been fascinating quantum information scientists. A constructive scheme has been given by Berry for remotely preparing a general pure state with a pure entangled state and finite classical communication. Based on this scheme, for high-dimensional systems it is possible to use a coding of the target state to optimize the classical communication cost. Unfortunately, for low-dimensional systems such as a pure qubit the coding method is inapplicable. Because qubit plays a central role in quantum information theory, we propose an optimization procedure which can be used to minimize the classical communication cost in the remote preparation of a general pure qubit. Interestingly, our optimization procedure is linked to the uniform arrangement of $N$ points on the Bloch sphere, which provides a geometric description.Comment: 4 pages, 3 figure

Large Extra Dimensions and Holography

The holographic principle asserts that the entropy of a system cannot exceed its boundary area in Planck units. However, conventional quantum field theory fails to describe such systems. In this Letter, we assume the existence of large $n$ extra dimensions and propose a relationship between UV and IR cutoffs in this case. We find that if $n=2$, this effective field theory could be a good description of holographic systems. If these extra dimensions are detected in future experiments, it will help to prove the validity of the holographic principle. We also discuss implications for the cosmological constant problem.Comment: Revtex, 4 page