Singlet Generation in Mixed State Quantum Networks

We study the generation of singlets in quantum networks with nodes initially sharing a finite number of partially entangled bipartite mixed states. We prove that singlets between arbitrary nodes in such networks can be created if and only if the initial states connecting the nodes have a particular form. We then generalize the method of entanglement percolation, previously developed for pure states, to mixed states of this form. As part of this, we find and compare different distillation protocols necessary to convert groups of mixed states shared between neighboring nodes of the network into singlets. In addition, we discuss protocols that only rely on local rules for the efficient connection of two remote nodes in the network via entanglement swapping. Further improvements of the success probability of singlet generation are developed by using particular forms of `quantum preprocessing' on the network. This includes generalized forms of entanglement swapping and we show how such strategies can be embedded in regular and hierarchical quantum networks.Comment: 17 pages, 21 figure

Recall of random and distorted positions: Implications for the theory of expertise.

This paper explores the question, important to the theory of expert performance, of the nature and number of chunks that chess experts hold in memory. It examines how memory contents determine players' abilities to reconstruct (a) positions from games, (b) positions distorted in various ways and (c) and random positions. Comparison of a computer simulation with a human experiment supports the usual estimate that chess Masters store some 50,000 chunks in memory. The observed impairment of recall when positions are modified by mirror image reflection, implies that each chunk represents a specific pattern of pieces in a specific location. A good account of the results of the experiments is given by the template theory proposed by Gobet and Simon (in press) as an extension of Chase and Simon's (1973a) initial chunking proposal, and in agreement with other recent proposals for modification of the chunking theory (Richman, Staszewski & Simon, 1995) as applied to various recall tasks

Discrepancy bounds for low-dimensional point sets

The class of $(t,m,s)$-nets and $(t,s)$-sequences, introduced in their most general form by Niederreiter, are important examples of point sets and sequences that are commonly used in quasi-Monte Carlo algorithms for integration and approximation. Low-dimensional versions of $(t,m,s)$-nets and $(t,s)$-sequences, such as Hammersley point sets and van der Corput sequences, form important sub-classes, as they are interesting mathematical objects from a theoretical point of view, and simultaneously serve as examples that make it easier to understand the structural properties of $(t,m,s)$-nets and $(t,s)$-sequences in arbitrary dimension. For these reasons, a considerable number of papers have been written on the properties of low-dimensional nets and sequences