Detecting topology change via correlations and entanglement from gauge/gravity correspondence

We compute a momentum space version of the entanglement spectrum and entanglement entropy of general Young tableau states, and one-point functions on Young tableau states. These physical quantities are used to measure the topology of the dual spacetime geometries in the context of gauge/gravity correspondence. The idea that Young tableau states can be obtained by superposing coherent states is explicitly verified. In this quantum superposition, a topologically distinct geometry is produced by superposing states dual to geometries with a trivial topology. Furthermore we have a refined bound for the overlap between coherent states and the rectangular Young tableau state, by using the techniques of symmetric groups and representations. This bound is exponentially suppressed by the total edge length of the Young tableau. It is also found that the norm squared of the overlaps is bounded above by inverse powers of the exponential of the entanglement entropies. We also compute the overlaps between Young tableau states and other states including squeezed states and multi-mode entangled states which have similarities with those appeared in quantum information theory.Comment: 48 pages. version in Journal of Mathematical Physic

Adding Logical Operators to Tree Pattern Queries on Graph-Structured Data

As data are increasingly modeled as graphs for expressing complex relationships, the tree pattern query on graph-structured data becomes an important type of queries in real-world applications. Most practical query languages, such as XQuery and SPARQL, support logical expressions using logical-AND/OR/NOT operators to define structural constraints of tree patterns. In this paper, (1) we propose generalized tree pattern queries (GTPQs) over graph-structured data, which fully support propositional logic of structural constraints. (2) We make a thorough study of fundamental problems including satisfiability, containment and minimization, and analyze the computational complexity and the decision procedures of these problems. (3) We propose a compact graph representation of intermediate results and a pruning approach to reduce the size of intermediate results and the number of join operations -- two factors that often impair the efficiency of traditional algorithms for evaluating tree pattern queries. (4) We present an efficient algorithm for evaluating GTPQs using 3-hop as the underlying reachability index. (5) Experiments on both real-life and synthetic data sets demonstrate the effectiveness and efficiency of our algorithm, from several times to orders of magnitude faster than state-of-the-art algorithms in terms of evaluation time, even for traditional tree pattern queries with only conjunctive operations.Comment: 16 page