Fundamental Limits to Coherent Photon Generation with Solid-State Atomlike Transitions

Coherent generation of indistinguishable single photons is crucial for many quantum communication and processing protocols. Solid-state realizations of two-level atomic transitions or three-level spin-$\Lambda$ systems offer significant advantages over their atomic counterparts for this purpose, albeit decoherence can arise due to environmental couplings. One popular approach to mitigate dephasing is to operate in the weak excitation limit, where excited state population is minimal and coherently scattered photons dominate over incoherent emission. Here we probe the coherence of photons produced using two-level and spin-$\Lambda$ solid-state systems. We observe that the coupling of the atomic-like transitions to the vibronic transitions of the crystal lattice is independent of driving strength and detuning. We apply a polaron master equation to capture the non-Markovian dynamics of the ground state vibrational manifolds. These results provide insight into the fundamental limitations for photon coherence from solid-state quantum emitters, with the consequence that deterministic single-shot quantum protocols are impossible and inherently probabilistic approaches must be embraced.Comment: 16 pages [with supplementary information], 8 figure

Epcast: Controlled Dissemination in Human-based Wireless Networks by means of Epidemic Spreading Models

Epidemics-inspired techniques have received huge attention in recent years from the distributed systems and networking communities. These algorithms and protocols rely on probabilistic message replication and redundancy to ensure reliable communication. Moreover, they have been successfully exploited to support group communication in distributed systems, broadcasting, multicasting and information dissemination in fixed and mobile networks. However, in most of the existing work, the probability of infection is determined heuristically, without relying on any analytical model. This often leads to unnecessarily high transmission overheads. In this paper we show that models of epidemic spreading in complex networks can be applied to the problem of tuning and controlling the dissemination of information in wireless ad hoc networks composed of devices carried by individuals, i.e., human-based networks. The novelty of our idea resides in the evaluation and exploitation of the structure of the underlying human network for the automatic tuning of the dissemination process in order to improve the protocol performance. We evaluate the results using synthetic mobility models and real human contacts traces

On the Convergence of Population Protocols When Population Goes to Infinity

Population protocols have been introduced as a model of sensor networks consisting of very limited mobile agents with no control over their own movement. A population protocol corresponds to a collection of anonymous agents, modeled by finite automata, that interact with one another to carry out computations, by updating their states, using some rules. Their computational power has been investigated under several hypotheses but always when restricted to finite size populations. In particular, predicates stably computable in the original model have been characterized as those definable in Presburger arithmetic. We study mathematically the convergence of population protocols when the size of the population goes to infinity. We do so by giving general results, that we illustrate through the example of a particular population protocol for which we even obtain an asymptotic development. This example shows in particular that these protocols seem to have a rather different computational power when a huge population hypothesis is considered.Comment: Submitted to Applied Mathematics and Computation. 200

Synaptic mechanisms of interference in working memory

Information from preceding trials of cognitive tasks can bias performance in the current trial, a phenomenon referred to as interference. Subjects performing visual working memory tasks exhibit interference in their trial-to-trial response correlations: the recalled target location in the current trial is biased in the direction of the target presented on the previous trial. We present modeling work that (a) develops a probabilistic inference model of this history-dependent bias, and (b) links our probabilistic model to computations of a recurrent network wherein short-term facilitation accounts for the dynamics of the observed bias. Network connectivity is reshaped dynamically during each trial, providing a mechanism for generating predictions from prior trial observations. Applying timescale separation methods, we can obtain a low-dimensional description of the trial-to-trial bias based on the history of target locations. The model has response statistics whose mean is centered at the true target location across many trials, typical of such visual working memory tasks. Furthermore, we demonstrate task protocols for which the plastic model performs better than a model with static connectivity: repetitively presented targets are better retained in working memory than targets drawn from uncorrelated sequences.Comment: 28 pages, 7 figure

Correlation-based model of artificially induced plasticity in motor cortex by a bidirectional brain-computer interface

Experiments show that spike-triggered stimulation performed with Bidirectional Brain-Computer-Interfaces (BBCI) can artificially strengthen connections between separate neural sites in motor cortex (MC). What are the neuronal mechanisms responsible for these changes and how does targeted stimulation by a BBCI shape population-level synaptic connectivity? The present work describes a recurrent neural network model with probabilistic spiking mechanisms and plastic synapses capable of capturing both neural and synaptic activity statistics relevant to BBCI conditioning protocols. When spikes from a neuron recorded at one MC site trigger stimuli at a second target site after a fixed delay, the connections between sites are strengthened for spike-stimulus delays consistent with experimentally derived spike time dependent plasticity (STDP) rules. However, the relationship between STDP mechanisms at the level of networks, and their modification with neural implants remains poorly understood. Using our model, we successfully reproduces key experimental results and use analytical derivations, along with novel experimental data. We then derive optimal operational regimes for BBCIs, and formulate predictions concerning the efficacy of spike-triggered stimulation in different regimes of cortical activity.Comment: 35 pages, 9 figure

Immunization strategies for epidemic processes in time-varying contact networks

Spreading processes represent a very efficient tool to investigate the structural properties of networks and the relative importance of their constituents, and have been widely used to this aim in static networks. Here we consider simple disease spreading processes on empirical time-varying networks of contacts between individuals, and compare the effect of several immunization strategies on these processes. An immunization strategy is defined as the choice of a set of nodes (individuals) who cannot catch nor transmit the disease. This choice is performed according to a certain ranking of the nodes of the contact network. We consider various ranking strategies, focusing in particular on the role of the training window during which the nodes' properties are measured in the time-varying network: longer training windows correspond to a larger amount of information collected and could be expected to result in better performances of the immunization strategies. We find instead an unexpected saturation in the efficiency of strategies based on nodes' characteristics when the length of the training window is increased, showing that a limited amount of information on the contact patterns is sufficient to design efficient immunization strategies. This finding is balanced by the large variations of the contact patterns, which strongly alter the importance of nodes from one period to the next and therefore significantly limit the efficiency of any strategy based on an importance ranking of nodes. We also observe that the efficiency of strategies that include an element of randomness and are based on temporally local information do not perform as well but are largely independent on the amount of information available

The Dynamics and Stability of Probabilistic Population Processes

We study here the dynamics and stability of Probabilistic Population Processes, via the differential equations approach. We provide a quite general model following the work of Kurtz [15] for approximating discrete processes with continuous differential equations. We show that it includes the model of Angluin et al. [1], in the case of very large populations. We require that the long-term behavior of the family of increasingly large discrete processes is a good approximation to the long-term behavior of the continuous process, i.e., we exclude population protocols that are extremely unstable such as parity-dependent decision processes. For the general model, we give a sufficient condition for stability that can be checked in polynomial time. We also study two interesting sub cases: (a) Protocols whose specifications (in our terms) are configuration independent. We show that they are always stable and that their eventual subpopulation percentages are actually a Markov Chain stationary distribution. (b) Protocols that have dynamics resembling virus spread. We show that their dynamics are actually similar to the well-known Replicator Dynamics of Evolutionary Games. We also provide a sufficient condition for stability in this case