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Since their inception, superconducting nanowire single-photon detectors have been enabling quantum optical applications and the rise of the photonic quantum industry. The evolution in the detector design and read-out strategies has led to the introduction of devices with a plurality of independent pixels, which have been able to operate with high system detection efficiency at high speed while also supporting photon number resolution capabilities. However, this comes at the cost of a complex readout that requires one coaxial cable for each pixel of the array. Here, we report a 28-pixel SNSPD with a dedicated parallel architecture that, while maintaining a simple readout with a single coaxial line, enables the detector to operate at high speed with low-performance degradation. The device shows a maximum single-photon efficiency (SDE) of 88% and is able to maintain its SDE above 50%, coupled with a timing jitter lower than 80~ps, up to a detection rate of 200 million counts per second (Mcps). The detector also provides state-of-the-art PNR performances with a 2-photon efficiency of 75% and a 3-photon efficiency of 60%.

The ``comma sequence'' starts with 1 and is defined by the property that if k and k' are consecutive terms, the two-digit number formed from the last digit of k and the first digit of k' is equal to the difference k'-k. If there is more than one such k', choose the smallest, but if there is no such k' the sequence terminates. The sequence begins 1, 12, 35, 94, 135, ... and, surprisingly, ends at term 2137453, which is 99999945. The paper analyzes the sequence and its generalizations to other starting values and other bases. A slight change in the rules allows infinitely long comma sequences to exist., Comment: 19 pages, 4 figures, 1 table. Corrected a formula, expanded discussion of an asymptotic estimate, other small changes

Superconducting-nanowire single-photon detectors (SNSPDs) have enabled the realization of several quantum optics technologies thanks to their high detection efficiency, low dark-counts, and fast recovery time. However, the widespread use of technologies such as linear optical quantum computing (LOQC), quasi-deterministic single photon sources and quantum repeaters requires faster detectors that can distinguish between different photon number states. Here, we report the fabrication of an SNSPD array composed of 14 independent pixels, achieving a system detection efficiency (SDE) of 90% in the telecom band. By reading each pixel of the array independently we show that the detector can detect telecom photons at 1.5 GHz with 45% absolute SDE. We exploit the dynamic PNR of the array to demonstrate accurate state reconstruction for different photon-number statistics for a wide range of light inputs, including operation with long-duration light pulses, as commonly obtained with some cavity-based sources. We show 2-photon and 3-photon fidelities of 74% and 57% respectively, which represent state-of-the-art results for fiber-coupled SNSPDs.

Quantum Key Distribution has made continuous progress over the last 20 years and is now commercially available. However, the secret key rates (SKR) are still limited to a few Mbps. Here, we present a custom multipixel superconducting nanowire single-photon detectors and fast acquisition and real-time key distillation electronics, removing two roadblocks and allowing an increase of the SKR of more than an order of magnitude. In combination with a simple 2.5 GHz clocked time-bin quantum key distribution system, we can generate secret keys at a rate of 64 Mbps over a distance of 10.0 km and at a rate of 3.0 Mbps over a distance of 102.4 km with real-time key distillation., Comment: 5 pages, 5 figures, submitted to Nature Photonics

Sharing rides could drastically improve the efficiency of car and taxi transportation. Unleashing such potential, however, requires understanding how urban parameters affect the fraction of individual trips that can be shared, a quantity that we call shareability. Using data on millions of taxi trips in New York City, San Francisco, Singapore, and Vienna, we compute the shareability curves for each city, and find that a natural rescaling collapses them onto a single, universal curve. We explain this scaling law theoretically with a simple model that predicts the potential for ride sharing in any city, using a few basic urban quantities and no adjustable parameters. Accurate extrapolations of this type will help planners, transportation companies, and society at large to shape a sustainable path for urban growth.

Taxi services are a vital part of urban transportation, and a considerable contributor to traffic congestion and air pollution causing substantial adverse effects on human health. Sharing taxi trips is a possible way of reducing the negative impact of taxi services on cities, but this comes at the expense of passenger discomfort quantifiable in terms of a longer travel time. Due to computational challenges, taxi sharing has traditionally been approached on small scales, such as within airport perimeters, or with dynamical ad-hoc heuristics. However, a mathematical framework for the systematic understanding of the tradeoff between collective benefits of sharing and individual passenger discomfort is lacking. Here we introduce the notion of shareability network which allows us to model the collective benefits of sharing as a function of passenger inconvenience, and to efficiently compute optimal sharing strategies on massive datasets. We apply this framework to a dataset of millions of taxi trips taken in New York City, showing that with increasing but still relatively low passenger discomfort, cumulative trip length can be cut by 40% or more. This benefit comes with reductions in service cost, emissions, and with split fares, hinting towards a wide passenger acceptance of such a shared service. Simulation of a realistic online system demonstrates the feasibility of a shareable taxi service in New York City. Shareability as a function of trip density saturates fast, suggesting effectiveness of the taxi sharing system also in cities with much sparser taxi fleets or when willingness to share is low., Comment: Main text: 6 pages, 3 figures, SI: 24 pages

Performance bounds for opportunistic networks have been derived in a number of recent papers for several key quantities, such as the expected delivery time of a unicast message, or the flooding time (a measure of how fast information spreads). However, to the best of our knowledge, none of the existing results is derived under a mobility model which is able to reproduce the power law+exponential tail dichotomy of the pairwise node inter-contact time distribution which has been observed in traces of several real opportunistic networks. The contributions of this paper are two-fold: first, we present a simple pairwise contact model -- called the Home-MEG model -- for opportunistic networks based on the observation made in previous work that pairs of nodes in the network tend to meet in very few, selected locations (home locations); this contact model is shown to be able to faithfully reproduce the power law+exponential tail dichotomy of inter-contact time. Second, we use the Home-MEG model to analyze flooding time in opportunistic networks, presenting asymptotic bounds on flooding time that assume different initial conditions for the existence of opportunistic links. Finally, our bounds provide some analytical evidences that the speed of information spreading in opportunistic networks can be much faster than that predicted by simple geometric mobility models.