ASP(AC): Answer Set Programming with Algebraic Constraints

Weighted Logic is a powerful tool for the specification of calculations over semirings that depend on qualitative information. Using a novel combination of Weighted Logic and Here-and-There (HT) Logic, in which this dependence is based on intuitionistic grounds, we introduce Answer Set Programming with Algebraic Constraints (ASP(AC)), where rules may contain constraints that compare semiring values to weighted formula evaluations. Such constraints provide streamlined access to a manifold of constructs available in ASP, like aggregates, choice constraints, and arithmetic operators. They extend some of them and provide a generic framework for defining programs with algebraic computation, which can be fruitfully used e.g. for provenance semantics of datalog programs. While undecidable in general, expressive fragments of ASP(AC) can be exploited for effective problem-solving in a rich framework. This work is under consideration for acceptance in Theory and Practice of Logic Programming.Comment: 32 pages, 16 pages are appendi

Verification of nonclassicality in phase space

Nonclassicality was introduced to examine if experimental observations can be explained with a classical theory. Although the formal definition of nonclassicality is known for several decades, there has been a lack of simple and complete criteria to check nonclassicality. In this work, some criteria are compared. Then, so-called nonclassicality quasiprobabilities are introduced, which allow a full examination of nonclassicality for any quantum state. Finally, some issues of the relation between nonclassicality and entanglement are discussed. All concepts are illustrated with experimental data.Wenn optische Experimente nicht mit klassischer Physik erklärt werden können, wird der Zustand des Lichts als nichtklassisch bezeichnet. Obwohl dieser Begriff schon lange bekannt ist, fehlten bisher vollständige, einfache Kriterien für seine Untersuchung. In dieser Arbeit werden zunächst einige Kriterien verglichen. Dann werden Quasiverteilungen eingeführt, die einen einfachen Nachweis der Nichtklassizität für beliebige Zustände erlauben. Am Ende werden einige Zusammenhänge zwischen Nichtklassizität und Verschränkung untersucht. Alle Methoden werden auf experimentelle Daten angewendet

Moments of nonclassicality quasiprobabilities

A method is introduced for the verification of nonclassicality in terms of moments of nonclassicality quasiprobability distributions. The latter are easily obtained from experimental data and will be denoted as nonclassicality moments. Their relation to normally-ordered moments is derived, which enables us to verify nonclassicality by using well established criteria. Alternatively, nonclassicality criteria are directly formulated in terms of nonclassicality moments. The latter converge in proper limits to the usually used criteria, as is illustrated for squeezing and sub-Poissonian photon statistics. Our theory also yields expectation values of any observable in terms of nonclassicality moments.Comment: 6 pages, 3 figure

Information or noise: How Twitter facilitates stock market information aggregation

We assess the relevance of Twitter for stock-relevant information dissemination in financial markets on the single stock level. We use a unique dataset including more than 12 million Twitter feeds linked to specific firms. Using intraday data for the computation of advanced trading metrics, such as effective spreads, intraday volatility, and a daily version of the microstructure variable probability of informed trading (PIN), we measure the impact of Twitter activity on trading and information dissemination. The PIN model indicates that more uninformed than informed traders rush to the market along with rising Twitter activity. These results indicate that Twitter serves as an excellent indicator of news that is relevant for the stock market. However, we show that Twitter does not lead traditional news channels. In contrast, Twitter activity follows the market and has no predictive power with regard to future stock trading volume or volatility on the single stock level

Photonic entanglement as a resource in quantum computation and quantum communication

Entanglement is an essential resource in current experimental implementations for quantum information processing. We review a class of experiments exploiting photonic entanglement, ranging from one-way quantum computing over quantum communication complexity to long-distance quantum communication. We then propose a set of feasible experiments that will underline the advantages of photonic entanglement for quantum information processing.Comment: 33 pages, 4 figures, OSA styl

A high-speed tunable beam splitter for feed-forward photonic quantum information processing

We realize quantum gates for path qubits with a high-speed, polarization-independent and tunable beam splitter. Two electro-optical modulators act in a Mach-Zehnder interferometer as high-speed phase shifters and rapidly tune its splitting ratio. We test its performance with heralded single photons, observing a polarization-independent interference contrast above 95%. The switching time is about 5.6 ns, and a maximal repetition rate is 2.5 MHz. We demonstrate tunable feed-forward operations of a single-qubit gate of path-encoded qubits and a two-qubit gate via measurement-induced interaction between two photons

Direct generation of photon triplets using cascaded photon-pair sources

Non-classical states of light, such as entangled photon pairs and number states, are essential for fundamental tests of quantum mechanics and optical quantum technologies. The most widespread technique for creating these quantum resources is the spontaneous parametric down-conversion (SPDC) of laser light into photon pairs. Conservation of energy and momentum in this process, known as phase-matching, gives rise to strong correlations which are used to produce two-photon entanglement in various degrees of freedom. It has been a longstanding goal of the quantum optics community to realise a source that can produce analogous correlations in photon triplets, but of the many approaches considered, none have been technically feasible. In this paper we report the observation of photon triplets generated by cascaded down-conversion. Here each triplet originates from a single pump photon, and therefore quantum correlations will extend over all three photons in a way not achievable with independently created photon pairs. We expect our photon-triplet source to open up new avenues of quantum optics and become an important tool in quantum technologies. Our source will allow experimental interrogation of novel quantum correlations, the post-selection free generation of tripartite entanglement without post- selection and the generation of heralded entangled-photon pairs suitable for linear optical quantum computing. Two of the triplet photons have a wavelength matched for optimal transmission in optical fibres, ideally suited for three-party quantum communication. Furthermore, our results open interesting regimes of non-linear optics, as we observe spontaneous down-conversion pumped by single photons, an interaction also highly relevant to optical quantum computing.Comment: 7 pages, 3 figures, 1 table; accepted by Natur