Measure of multipartite entanglement with computable lower bounds

In this paper, we present a measure of multipartite entanglement ($k$-nonseparable), $k$-ME concurrence $C_{k-\mathrm{ME}}(\rho)$ that unambiguously detects all $k$-nonseparable states in arbitrary dimensions, where the special case, 2-ME concurrence $C_{2-\mathrm{ME}}(\rho)$, is a measure of genuine multipartite entanglement. The new measure $k$-ME concurrence satisfies important characteristics of an entanglement measure including entanglement monotone, vanishing on $k$-separable states, convexity, subadditivity and strictly greater than zero for all $k$-nonseparable states. Two powerful lower bounds on this measure are given. These lower bounds are experimentally implementable without quantum state tomography and are easily computable as no optimization or eigenvalue evaluation is needed. We illustrate detailed examples in which the given bounds perform better than other known detection criteria.Comment: 12 pages, 3 figure

Kosterlitz-Thouless and Potts transitions in a generalized XY model

We present extensive numerical simulations of a generalized XY model with nematic-like terms recently proposed by Poderoso {\it et al} [PRL 106(2011)067202]. Using finite size scaling and focusing on the $q=3$ case, we locate the transitions between the paramagnetic (P), the nematic-like (N) and the ferromagnetic (F) phases. The results are compared with the recently derived lower bounds for the P-N and P-F transitions. While the P-N transition is found to be very close to the lower bound, the P-F transition occurs significantly above the bound. Finally, the transition between the nematic-like and the ferromagnetic phases is found to belong to the 3-states Potts universality class.Comment: Extended and updated version of arXiv:1207.3447v

Competing nematic interactions in a generalized XY model in two and three dimensions

We study a generalization of the XY model with an additional nematic-like term through extensive numerical simulations and finite-size techniques, both in two and three dimensions. While the original model favors local alignment, the extra term induces angles of $2\pi/q$ between neighboring spins. We focus here on the $q=8$ case (while presenting new results for other values of $q$ as well) whose phase diagram is much richer than the well known $q=2$ case. In particular, the model presents not only continuous, standard transitions between Berezinskii-Kosterlitz-Thouless (BKT) phases as in $q=2$, but also infinite order transitions involving intermediate, competition driven phases absent for $q=2$ and 3. Besides presenting multiple transitions, our results show that having vortices decoupling at a transition is not a suficient condition for it to be of BKT type.Comment: 13 pages, 16 figure

Detection of genuinely entangled and non-separable nn-partite quantum states

We investigate the detection of entanglement in $n$-partite quantum states. We obtain practical separability criteria to identify genuinely entangled and non-separable mixed quantum states. No numerical optimization or eigenvalue evaluation is needed, and our criteria can be evaluated by simple computations involving components of the density matrix. We provide examples in which our criteria perform better than all known separability criteria. Specifically, we are able to detect genuine $n$-partite entanglement which has previously not been identified. In addition, our criteria can be used in today's experiment.Comment: 8 pages, one figur

Model-driven Enterprise Systems Configuration

Enterprise Systems potentially lead to significant efficiency gains but require a well-conducted configuration process. A promising idea to manage and simplify the configuration process is based on the premise of using reference models for this task. Our paper continues along this idea and delivers a two-fold contribution: first, we present a generic process for the task of model-driven Enterprise Systems configuration including the steps of (a) Specification of configurable reference models, (b) Configuration of configurable reference models, (c) Transformation of configured reference models to regular build time models, (d) Deployment of the generated build time models, (e) Controlling of implementation models to provide input to the configuration, and (f) Consolidation of implementation models to provide input to reference model specification. We discuss inputs and outputs as well as the involvement of different roles and validation mechanisms. Second, we present an instantiation case of this generic process for Enterprise Systems configuration based on Configurable EPCs

Efficient kk-separability criteria for mixed multipartite quantum states

We investigate classification and detection of entanglement of multipartite quantum states in a very general setting, and obtain efficient $k$-separability criteria for mixed multipartite states in arbitrary dimensional quantum systems. These criteria can be used to distinguish $n-1$ different classes of multipartite inseparable states and can detect many important multipartite entangled states such as GHZ states, W states, anti W states, and mixtures thereof. They detect $k$-nonseparable $n$-partite quantum states which have previously not been identified. Here $k=2,3,\cdots,n$. No optimization or eigenvalue evaluation is needed, and our criteria can be evaluated by simple computations involving components of the density matrix. Most importantly, they can be implemented in today's experiments by using at most $\mathcal{O}(n^2)$ local measurements.Comment: 6 pages, 4 figure

Modular parallel transport of multiple intervals in 1+1-dimensional free fermion theory

Modular parallel transport is a generalization of Berry phases, applied to modular (entanglement) Hamiltonians. Here we initiate the study of modular parallel transport for disjoint field theory regions. We study modular parallel transport in the kinematic space of multi-interval regions in the vacuum of 1+1-dimensional free fermion theory--one of the few theories for which modular Hamiltonians on disjoint regions are known. We compute explicitly the generators of modular parallel transport, and explain why their relatively simple form follows from a half-sided modular inclusion. We also compute explicitly the curvature two-form of modular parallel transport. We contrast all calculations with the expected behavior of modular parallel transport in holographic theories, emphasizing the role of non-local terms that couple distinct intervals.Comment: 24 pages, 5 figure

Partially Observable Stochastic Games with Neural Perception Mechanisms

Stochastic games are a well established model for multi-agent sequential decision making under uncertainty. In reality, though, agents have only partial observability of their environment, which makes the problem computationally challenging, even in the single-agent setting of partially observable Markov decision processes. Furthermore, in practice, agents increasingly perceive their environment using data-driven approaches such as neural networks trained on continuous data. To tackle this problem, we propose the model of neuro-symbolic partially-observable stochastic games (NS-POSGs), a variant of continuous-space concurrent stochastic games that explicitly incorporates perception mechanisms. We focus on a one-sided setting, comprising a partially-informed agent with discrete, data-driven observations and a fully-informed agent with continuous observations. We present a new point-based method, called one-sided NS-HSVI, for approximating values of one-sided NS-POSGs and implement it based on the popular particle-based beliefs, showing that it has closed forms for computing values of interest. We provide experimental results to demonstrate the practical applicability of our method for neural networks whose preimage is in polyhedral form.Comment: 41 pages, 5 figure

Probabilistic model checking for strategic equilibria-based decision making:advances and challenges

Game-theoretic concepts have been extensively studied in economics to provide insight into competitive behaviour and strategic decision making. As computing systems increasingly involve concurrently acting autonomous agents, game-theoretic approaches are becoming widespread in computer science as a faithful modelling abstraction. These techniques can be used to reason about the competitive or collaborative behaviour of multiple rational agents with distinct goals or objectives. This paper provides an overview of recent advances in developing a modelling, verification and strategy synthesis framework for concurrent stochastic games implemented in the probabilistic model checker PRISM-games. This is based on a temporal logic that supports finite- and infinite-horizon temporal properties in both a zero-sum and nonzero-sum setting, the latter using Nash and correlated equilibria with respect to two optimality criteria, social welfare and social fairness. We summarise the key concepts, logics and algorithms and the currently available tool support. Future challenges and recent progress in adapting the framework and algorithmic solutions to continuous environments and neural networks are also outlined