32,749 research outputs found
EPR Pairs, Local Projections and Quantum Teleportation in Holography
In this paper we analyze three quantum operations in two dimensional
conformal field theories (CFTs): local projection measurements, creations of
partial entanglement between two CFTs, and swapping of subsystems between two
CFTs. We also give their holographic duals and study time evolutions of
entanglement entropy. By combining these operations, we present an analogue of
quantum teleportation between two CFTs and give its holographic realization. We
introduce a new quantity to probe tripartite entanglement by using local
projection measurement.Comment: 61 pages, 24 figures. v2: comments and refs added. v3: minor
correction
A Unifying Model for Representing Time-Varying Graphs
Graph-based models form a fundamental aspect of data representation in Data
Sciences and play a key role in modeling complex networked systems. In
particular, recently there is an ever-increasing interest in modeling dynamic
complex networks, i.e. networks in which the topological structure (nodes and
edges) may vary over time. In this context, we propose a novel model for
representing finite discrete Time-Varying Graphs (TVGs), which are typically
used to model dynamic complex networked systems. We analyze the data structures
built from our proposed model and demonstrate that, for most practical cases,
the asymptotic memory complexity of our model is in the order of the
cardinality of the set of edges. Further, we show that our proposal is an
unifying model that can represent several previous (classes of) models for
dynamic networks found in the recent literature, which in general are unable to
represent each other. In contrast to previous models, our proposal is also able
to intrinsically model cyclic (i.e. periodic) behavior in dynamic networks.
These representation capabilities attest the expressive power of our proposed
unifying model for TVGs. We thus believe our unifying model for TVGs is a step
forward in the theoretical foundations for data analysis of complex networked
systems.Comment: Also appears in the Proc. of the IEEE International Conference on
Data Science and Advanced Analytics (IEEE DSAA'2015
Iterated functions and the Cantor set in one dimension
In this paper we consider the long-term behavior of points in
under iterations of continuous functions. We show that, given any Cantor set
embedded in , there exists a continuous function
such that the points that are bounded under
iterations of are just those points in . In the course of
this, we find a striking similarity between the way in which we construct the
Cantor middle-thirds set, and the way in which we find the points bounded under
iterations of certain continuous functions
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