Random numbers are a valuable component in diverse applications that range from simulations(1) over gambling to cryptography(2,3). The quest for true randomness in these applications has engendered a large variety of different proposals for producing random numbers based on the foundational unpredictability of quantum mechanics(4-11). However, most approaches do not consider that a potential adversary could have knowledge about the generated numbers, so the numbers are not verifiably random and unique(12-15). Here we present a simple experimental setup based on homodyne measurements that uses the purity of a continuous-variable quantum vacuum state to generate unique random numbers. We use the intrinsic randomness in measuring the quadratures of a mode in the lowest energy vacuum state, which cannot be correlated to any other state. The simplicity of our source, combined with its verifiably unique randomness, are important attributes for achieving high-reliability, high-speed and low-cost quantum random number generators

Frequency conversion (FC) and type-II parametric down-conversion (PDC) processes serve as basic building blocks for the implementation of quantum optical experiments: type-II PDC enables the efficient creation of quantum states such as photon-number states and Einstein-Podolsky-Rosen (EPR)-states. FC gives rise to technologies enabling efficient atom-photon coupling, ultrafast pulse gates and enhanced detection schemes. However, despite their widespread deployment, their theoretical treatment remains challenging. Especially the multi-photon components in the high-gain regime as well as the explicit time-dependence of the involved Hamiltonians hamper an efficient theoretical description of these nonlinear optical processes. In this paper, we investigate these effects and put forward two models that enable a full description of FC and type-II PDC in the high-gain regime. We present a rigorous numerical model relying on the solution of coupled integro-differential equations that covers the complete dynamics of the process. As an alternative, we develop a simplified model that, at the expense of neglecting time-ordering effects, enables an analytical solution. While the simplified model approximates the correct 4

We discuss the spectral structure and decomposition of multi-photon states. Ordinarily 'multiphoton states' and 'Fock states' are regarded as synonymous. However, when the spectral degrees of freedom are included this is not the case, and the class of 'multi-photon' states is much broader than the class of 'Fock' states. We discuss the criteria for a state to be considered a Fock state. We then address the decomposition of general multi-photon states into bases of orthogonal eigenmodes, building on existing multi-mode theory, and introduce an occupation number representation that provides an elegant description of such states. This representation allows us to work in bases imposed by experimental constraints, simplifying calculations in many situations. Finally we apply this technique to several example situations, which are highly relevant for state of the art experiments. These include Hong-Ou-Mandel interference, spectral filtering, finite bandwidth photo-detection, homodyne detection and the conditional preparation of Schrödinger Kitten and Fock states. Our techniques allow for very simple descriptions of each of these examples.

Abstract-Effective software engineering demands a coordinated effort. Unfortunately, a comprehensive view on developer coordination is rarely available to support software-engineering decisions, despite the significant implications on software quality, software architecture, and developer productivity. We present a fine-grained, verifiable, and fully automated approach to capture a view on developer coordination, based on commit information and source-code structure, mined from version-control systems. We apply methodology from network analysis and machine learning to identify developer communities automatically. Compared to previous work, our approach is fine-grained, and identifies statistically significant communities using order-statistics and a community-verification technique based on graph conductance. To demonstrate the scalability and generality of our approach, we analyze ten open-source projects with complex and active histories, written in various programming languages. By surveying 53 open-source developers from the ten projects, we validate the authenticity of inferred community structure with respect to reality. Our results indicate that developers of open-source projects form statistically significant community structures and this particular view on collaboration largely coincides with developers' perceptions of real-world collaboration.