Constant-Space Population Protocols for Uniform Bipartition

In this paper, we consider a uniform bipartition problem in a population protocol model. The goal of the uniform bipartition problem is to divide a population into two groups of the same size. We study the problem under various assumptions: 1) a population with or without a base station, 2) weak or global fairness, 3) symmetric or asymmetric protocols, and 4) designated or arbitrary initial states. As a result, we completely clarify constant-space solvability of the uniform bipartition problem and, if solvable, propose space-optimal protocols

Uniform Partition in Population Protocol Model Under Weak Fairness

We focus on a uniform partition problem in a population protocol model. The uniform partition problem aims to divide a population into k groups of the same size, where k is a given positive integer. In the case of k=2 (called uniform bipartition), a previous work clarified space complexity under various assumptions: 1) an initialized base station (BS) or no BS, 2) weak or global fairness, 3) designated or arbitrary initial states of agents, and 4) symmetric or asymmetric protocols, except for the setting that agents execute a protocol from arbitrary initial states under weak fairness in the model with an initialized base station. In this paper, we clarify the space complexity for this remaining setting. In this setting, we prove that P states are necessary and sufficient to realize asymmetric protocols, and that P+1 states are necessary and sufficient to realize symmetric protocols, where P is the known upper bound of the number of agents. From these results and the previous work, we have clarified the solvability of the uniform bipartition for each combination of assumptions. Additionally, we newly consider an assumption on a model of a non-initialized BS and clarify solvability and space complexity in the assumption. Moreover, the results in this paper can be applied to the case that k is an arbitrary integer (called uniform k-partition)

Uniform Bipartition in the Population Protocol Model with Arbitrary Communication Graphs

In this paper, we focus on the uniform bipartition problem in the population protocol model. This problem aims to divide a population into two groups of equal size. In particular, we consider the problem in the context of arbitrary communication graphs. As a result, we investigate the solvability of the uniform bipartition problem with arbitrary communication graphs when agents in the population have designated initial states, under various assumptions such as the existence of a base station, symmetry of the protocol, and fairness of the execution. When the problem is solvable, we present protocols for uniform bipartition. When global fairness is assumed, the space complexity of our solutions is tight

Scalability of GHZ and random-state entanglement in the presence of decoherence

We derive analytical upper bounds for the entanglement of generalized Greenberger-Horne-Zeilinger states coupled to locally depolarizing and dephasing environments, and for local thermal baths of arbitrary temperature. These bounds apply for any convex quantifier of entanglement, and exponential entanglement decay with the number of constituent particles is found. The bounds are tight for depolarizing and dephasing channels. We also show that randomly generated initial states tend to violate these bounds, and that this discrepancy grows with the number of particles.Comment: 9 pages, 3 figure

Diverse applications of the Quantum Walk model in Quantum Information: a theoretical and experimental analysis in the optical framework

Quantum Walks have been a very important model in the last thirty years, after their first definition and rigorous description. The analysis of the many possible variations of their behavior has delivered a plethora of solutions and platforms for the many diverse fields of investigation. The applications of the Quantum Walk model spreads from the development of Quantum Algorithm, to the modeling and simulation of systems of the most diverse nature, such as solid state or biological systems. In general, it helped developing a well-established quantum (or coherent) propagation model, which is useful both inside and outside physics. In this thesis, we focus on the study of disordered Quantum Walks, in order to get better understanding of the inuence of Quantum Walk disordered dynamics to non-classical correlations and propagating quantum information. Afterwards, we generalize this dynamical approach to Quantum Information processing, developing a Quantum Receiver for Quantum State Discrimination featuring a time multiplexing structure and we investigate the potentiality of this Quantum Walk inspired framework in the field of Quantum State Discrimination, through the developing and realization of experimental protocols characterized by increasing complexity. We also report on some apparent deviations from this path, although still aimed at the transfer of our expertise, built in previous investigations, to the study of new models and more complex quantum systems

Whole mitochondrial genome sequencing of domestic horses reveals incorporation of extensive wild horse diversity during domestication

<p>Abstract</p> <p>Background</p> <p>DNA target enrichment by micro-array capture combined with high throughput sequencing technologies provides the possibility to obtain large amounts of sequence data (e.g. whole mitochondrial DNA genomes) from multiple individuals at relatively low costs. Previously, whole mitochondrial genome data for domestic horses (<it>Equus caballus</it>) were limited to only a few specimens and only short parts of the mtDNA genome (especially the hypervariable region) were investigated for larger sample sets.</p> <p>Results</p> <p>In this study we investigated whole mitochondrial genomes of 59 domestic horses from 44 breeds and a single Przewalski horse (<it>Equus przewalski</it>) using a recently described multiplex micro-array capture approach. We found 473 variable positions within the domestic horses, 292 of which are parsimony-informative, providing a well resolved phylogenetic tree. Our divergence time estimate suggests that the mitochondrial genomes of modern horse breeds shared a common ancestor around 93,000 years ago and no later than 38,000 years ago. A Bayesian skyline plot (BSP) reveals a significant population expansion beginning 6,000-8,000 years ago with an ongoing exponential growth until the present, similar to other domestic animal species. Our data further suggest that a large sample of wild horse diversity was incorporated into the domestic population; specifically, at least 46 of the mtDNA lineages observed in domestic horses (73%) already existed before the beginning of domestication about 5,000 years ago.</p> <p>Conclusions</p> <p>Our study provides a window into the maternal origins of extant domestic horses and confirms that modern domestic breeds present a wide sample of the mtDNA diversity found in ancestral, now extinct, wild horse populations. The data obtained allow us to detect a population expansion event coinciding with the beginning of domestication and to estimate both the minimum number of female horses incorporated into the domestic gene pool and the time depth of the domestic horse mtDNA gene pool.</p

Interacting bosonic flux ladders with a synthetic dimension: Ground-state phases and quantum quench dynamics

Flux ladders constitute the minimal setup enabling a systematic understanding of the rich physics of interacting particles subjected simultaneously to strong magnetic fields and a lattice potential. In this paper, the ground-state phase diagram of a flux-ladder model is mapped out using extensive density-matrix renormalization-group simulations. The emphasis is put on parameters which can be experimentally realized exploiting the internal states of potassium atoms as a synthetic dimension. The focus is on accessible observables such as the chiral current and the leg-population imbalance. Considering a particle filling of one boson per rung, we report the existence of a Mott-insulating Meissner phase as well as biased-ladder phases on top of superfluids and Mott insulators. Furthermore, we demonstrate that quantum quenches from suitably chosen initial states can be used to probe the equilibrium properties in the transient dynamics. Concretely, we consider the instantaneous turning on of hopping matrix elements along the rungs or legs in the synthetic flux-ladder model, with different initial particle distributions. We show that clear signatures of the biased-ladder phase can be observed in the transient dynamics. Moreover, the behavior of the chiral current in the transient dynamics is discussed. The results presented in this paper provide guidelines for future implementations of flux ladders in experimental setups exploiting a synthetic dimension.Comment: as published, with plotted data in json forma