- Aug 22 2017 quant-ph arXiv:1708.06144v1In this work, we demonstrate a new way to perform classical multiparty computing amongst parties with limited computational resources. Our method harnesses quantum resources to increase the computational power of the individual parties. We show how a set of clients restricted to linear classical processing are able to jointly compute a non-linear multivariable function that lies beyond their individual capabilities. The clients are only allowed to perform classical XOR gates and single-qubit gates on quantum states. We also examine the type of security that can be achieved in this limited setting. Finally, we provide a proof-of-concept implementation using photonic qubits, that allows four clients to compute a specific example of a multiparty function, the pairwise AND.
- We consider the problem of quantum state certification, where one is given $n$ copies of an unknown $d$-dimensional quantum mixed state $\rho$, and one wants to test whether $\rho$ is equal to some known mixed state $\sigma$ or else is $\epsilon$-far from $\sigma$. The goal is to use notably fewer copies than the $\Omega(d^2)$ needed for full tomography on $\rho$ (i.e., density estimation). We give two robust state certification algorithms: one with respect to fidelity using $n = O(d/\epsilon)$ copies, and one with respect to trace distance using $n = O(d/\epsilon^2)$ copies. The latter algorithm also applies when $\sigma$ is unknown as well. These copy complexities are optimal up to constant factors.
- A pure multipartite quantum state is called absolutely maximally entangled (AME), if all reductions obtained by tracing out at least half of its parties are maximally mixed. However, the existence of such states is in many cases unclear. With the help of the weight enumerator machinery known from quantum error correcting codes and the generalized shadow inequalities, we obtain new bounds on the existence of AME states in higher dimensions. To complete the treatment on the weight enumerator machinery, the quantum MacWilliams identity is derived in the Bloch representation.
- Aug 22 2017 quant-ph arXiv:1708.05901v1We consider the inverse eigenvalue problem for entanglement witnesses, which asks for a characterization of their possible spectra (or equivalently, of the possible spectra resulting from positive linear maps of matrices). We completely solve this problem in the two-qubit case and we derive a large family of new necessary conditions on the spectra in arbitrary dimensions. We also establish a natural duality relationship with the set of absolutely separable states, and we completely characterize witnesses (i.e., separating hyperplanes) of that set when one of the local dimensions is 2.
- Aug 22 2017 cs.CC arXiv:1708.05786v1We give an adaptive algorithm which tests whether an unknown Boolean function $f\colon \{0, 1\}^n \to\{0, 1\}$ is unate, i.e. every variable of $f$ is either non-decreasing or non-increasing, or $\epsilon$-far from unate with one-sided error using $\widetilde{O}(n^{3/4}/\epsilon^2)$ queries. This improves on the best adaptive $O(n/\epsilon)$-query algorithm from Baleshzar, Chakrabarty, Pallavoor, Raskhodnikova and Seshadhri when $1/\epsilon \ll n^{1/4}$. Combined with the $\widetilde{\Omega}(n)$-query lower bound for non-adaptive algorithms with one-sided error of [CWX17, BCPRS17], we conclude that adaptivity helps for the testing of unateness with one-sided error. A crucial component of our algorithm is a new subroutine for finding bi-chromatic edges in the Boolean hypercube called adaptive edge search.
- Zero-field nuclear magnetic resonance (NMR) provides complementary analysis modalities to those of high-field NMR and allows for ultra-high-resolution spectroscopy and measurement of untruncated spin-spin interactions. Unlike for the high-field case, however, universal quantum control -- the ability to perform arbitrary unitary operations -- has not been experimentally demonstrated in zero-field NMR. This is because the Larmor frequency for all spins is identically zero at zero field, making it challenging to individually address different spin species. We realize a composite-pulse technique for arbitrary independent rotations of $^1$H and $^{13}$C spins in a two-spin system. Quantum-information-inspired randomized benchmarking and state tomography are used to evaluate the quality of the control. We experimentally demonstrate single-spin control for $^{13}$C with an average gate fidelity of $0.9960(2)$ and two-spin control via a controlled-not (CNOT) gate with an estimated fidelity of $0.99$. The combination of arbitrary single-spin gates and a CNOT gate is sufficient for universal quantum control of the nuclear spin system. The realization of complete spin control in zero-field NMR is an essential step towards applications to quantum simulation, entangled-state-assisted quantum metrology, and zero-field NMR spectroscopy.
- We study a generalized nonlocal theory of gravity which, in specific limits, can become either the curvature non-local or teleparallel non-local theory. Using the Noether Symmetry Approach, we find that the coupling functions coming from the non-local terms are constrained to be either exponential or linear in form. It is well known that in some non-local theories, a certain kind of exponential non-local couplings are needed in order to achieve a renormalizable theory. In this paper, we explicitly show that this kind of coupling does not need to by introduced by hand, instead, it appears naturally from the symmetries of the Lagrangian in flat Friedmann-Robertson-Walker cosmology. Finally, we find de-Sitter and power law cosmological solutions for different nonlocal theories. The symmetries for the generalized non-local theory is also found and some cosmological solutions are also achieved under the full theory.
- Aug 22 2017 cs.CV arXiv:1708.06297v1To efficiently establish training databases for machine learning methods, collaborative and crowdsourcing platforms have been investigated to collectively tackle the annotation effort. However, when this concept is ported to the medical imaging domain, reading expertise will have a direct impact on the annotation accuracy. In this study, we examine the impact of expertise and the amount of available annotations on the accuracy outcome of a liver segmentation problem in an abdominal computed tomography (CT) image database. In controlled experiments, we study this impact for different types of weak annotations. To address the decrease in accuracy associated with lower expertise, we propose a method for outlier correction making use of a weakly labelled atlas. Using this approach, we demonstrate that weak annotations subject to high error rates can achieve a similarly high accuracy as state-of-the-art multi-atlas segmentation approaches relying on a large amount of expert manual segmentations. Annotations of this nature can realistically be obtained from a non-expert crowd and can potentially enable crowdsourcing of weak annotation tasks for medical image analysis.
- We model the spread of news as a social learning game on a network. Agents can either endorse or oppose a claim made in a piece of news, which itself may be either true or false. Agents base their decision on a private signal and their neighbors' past actions. Given these inputs, agents follow strategies derived via multi-agent deep reinforcement learning and receive utility from acting in accordance with the veracity of claims. Our framework yields strategies with agent utility close to a theoretical, Bayes optimal benchmark, while remaining flexible to model re-specification. Optimized strategies allow agents to correctly identify most false claims, when all agents receive unbiased private signals. However, an adversary's attempt to spread fake news by targeting a subset of agents with a biased private signal can be successful. Even more so when the adversary has information about agents' network position or private signal. When agents are aware of the presence of an adversary they re-optimize their strategies in the training stage and the adversary's attack is less effective. Hence, exposing agents to the possibility of fake news can be an effective way to curtail the spread of fake news in social networks. Our results also highlight that information about the users' private beliefs and their social network structure can be extremely valuable to adversaries and should be well protected.
- Aug 22 2017 quant-ph arXiv:1708.06208v1We study the behavior of non-Markovianity with respect to the localization of the initial environmental state. The "amount" of non-Markovianity is measured using divisibility and distinguishability as indicators, employing several schemes to construct the measures. The system used is a qubit coupled to an environment modeled by an Ising spin chain kicked by ultra-short pulses of a magnetic field. In the integrable regime, non-Markovianity and localization do not have a simple relation, but as the chaotic regime is approached, simple relations emerge, which we explore in detail. We also study the non-Markovianity measures in the space of the parameters of the spin coherent states and point out that the pattern that appears is robust under the choice of the interaction Hamiltonian but does not have a KAM-like phase-space structure.
- Aug 22 2017 astro-ph.CO arXiv:1708.06139v1In both WMAP and Planck observations on the temperature anisotropy of cosmic microwave background (CMB) radiation a number of large-scale anomalies were discovered in the past years, including the CMB parity asymmetry in the low multipoles. By defining a directional statistics, we find that the CMB parity asymmetry is directional dependent, and the preferred axis is stable, which means that it is independent of the chosen CMB map, the definition of the statistic, or the CMB masks. Meanwhile, we find that this preferred axis strongly aligns with those of the CMB quadrupole, octopole, as well as those of other large-scale observations. In addition, all of them aligns with the CMB kinematic dipole, which hints to the non-cosmological origin of these directional anomalies in cosmological observations.
- Aug 22 2017 quant-ph physics.optics arXiv:1708.06101v1Quantum information science and quantum information technology have seen a virtual explosion world-wide. It is all based on the observation that fundamental quantum phenomena on the individual particle or system-level lead to completely novel ways of encoding, processing and transmitting information. Quantum mechanics, a child of the first third of the 20th century, has found numerous realizations and technical applications, much more than was thought at the beginning. Decades later, it became possible to do experiments with individual quantum particles and quantum systems. This was due to technological progress, and for light in particular, the development of the laser. Hitherto, nearly all experiments and also nearly all realizations in the fields have been performed with qubits, which are two-level quantum systems. We suggest that this limitation is again mainly a technological one, because it is very difficult to create, manipulate and measure more complex quantum systems. Here, we provide a specific overview of some recent developments with higher-dimensional quantum systems. We mainly focus on Orbital Angular Momentum (OAM) states of photons and possible applications in quantum information protocols. Such states form discrete higher-dimensional quantum systems, also called qudits. Specifically, we will first address the question what kind of new fundamental properties exist and the quantum information applications which are opened up by such novel systems. Then we give an overview of recent developments in the field by discussing several notable experiments over the past 2-3 years. Finally, we conclude with several important open questions which will be interesting for investigations in the future.
- Aug 22 2017 quant-ph arXiv:1708.06057v1Aharonov, Jones, and Landau [Algorithmica 55, 395 (2009)] have presented a polynomial quantum algorithm for approximating the Jones polynomial. We investigate the bipartite entanglement properties in AJL's algorithm for three-strand braids. We re-describe AJL's algorithm as an equivalent algorithm which involves three work qubits in some mixed state coupled to a single control qubit. Furthermore, we use the Peres entanglement criterion to study the entanglement features of the state before measurements present in the re-described algorithm for all bipartitions. We show that the state is a product state relative to the bipartition between the first work qubit and the others. And it has no entanglement between the control qubit and work ones. We also prove a sufficient and necessary condition for its entanglement between the second (third) work qubit and the others. Moreover, we discuss the relation between its bipartite entanglement and elementary crossings in the three-strand braid group. We find that braids whose trace closures are topologically identical may have different entanglement properties in AJL's algorithm.
- Aug 22 2017 cs.NE arXiv:1708.06008v1We review Boltzmann machines and energy-based models. A Boltzmann machine defines a probability distribution over binary-valued patterns. One can learn parameters of a Boltzmann machine via gradient based approaches in a way that log likelihood of data is increased. The gradient and Laplacian of a Boltzmann machine admit beautiful mathematical representations, although computing them is in general intractable. This intractability motivates approximate methods, including Gibbs sampler and contrastive divergence, and tractable alternatives, namely energy-based models.
- Training large vocabulary Neural Network Language Models (NNLMs) is a difficult task due to the explicit requirement of the output layer normalization, which typically involves the evaluation of the full softmax function over the complete vocabulary. This paper proposes a Batch Noise Contrastive Estimation (B-NCE) approach to alleviate this problem. This is achieved by reducing the vocabulary, at each time step, to the target words in the batch and then replacing the softmax by the noise contrastive estimation approach, where these words play the role of targets and noise samples at the same time. In doing so, the proposed approach can be fully formulated and implemented using optimal dense matrix operations. Applying B-NCE to train different NNLMs on the Large Text Compression Benchmark (LTCB) and the One Billion Word Benchmark (OBWB) shows a significant reduction of the training time with no noticeable degradation of the models performance. This paper also presents a new baseline comparative study of different standard NNLMs on the large OBWB on a single Titan-X GPU.
- Aug 22 2017 cs.CL arXiv:1708.05956v1We present a novel end-to-end trainable neural network model for task-oriented dialog systems. The model is able to track dialog state, issue API calls to knowledge base (KB), and incorporate structured KB query results into system responses to successfully complete task-oriented dialogs. The proposed model produces well-structured system responses by jointly learning belief tracking and KB result processing conditioning on the dialog history. We evaluate the model in a restaurant search domain using a dataset that is converted from the second Dialog State Tracking Challenge (DSTC2) corpus. Experiment results show that the proposed model can robustly track dialog state given the dialog history. Moreover, our model demonstrates promising results in producing appropriate system responses, outperforming prior end-to-end trainable neural network models using per-response accuracy evaluation metrics.
- Aug 22 2017 gr-qc arXiv:1708.05900v1Two different ways of generalizing Einstein's General Theory of Relativity with a cosmological constant to Brans-Dicke type scalar-tensor theories are investigated in the linearized field approximation. In the first case a cosmological constant term is coupled to a scalar field linearly whereas in the second case an arbitrary potential plays the role of a variable cosmological term. We see that former configuration leads to a massless scalar field whereas latter leads to a massive scalar field. General solutions of these linearized field equations for both cases are obtained corresponding to a static point mass. Geodesics of these solutions are discussed for two physically relevant cases. First one is the advance of the perihelion and the second one is the deflection of light rays. The contribution of the scalar field, cosmological term or minimum of the potential to these phenomena are derived.
- Aug 22 2017 cond-mat.stat-mech cond-mat.dis-nn arXiv:1708.05876v1We use invasion percolation to compute numerical values for bond and site percolation thresholds $p_c$ (existence of an infinite cluster) and $p_u$ (uniqueness of the infinite cluster) of tesselations $\{P,Q\}$ of the hyperbolic plane, where $Q$ faces meet at each vertex and each face is a $P$-gon. Our values are accurate to six or seven decimal places, allowing us to explore their functional dependency on $P$ and $Q$ and to numerically compute critical exponents. We also prove rigorous upper and lower bounds for $p_c$ and $p_u$ that can be used to find the scaling of both thresholds as a function of $P$ and $Q$.
- Aug 22 2017 gr-qc astro-ph.CO arXiv:1708.05739v1As is well known, some aspects of General Relativity and Cosmology can be reproduced without even using Einstein's equation. As an illustration, the 0 - 0 component of the Schwarzschild space can be obtained by the requirement that the geodesic of slowly mov- ing particles match the Newtonian equation. Given this result, we shall show here that the remaining component (grr) can be obtained by requiring that the inside of a Newtonian ball of dust matched at a free falling radius with the external space of unspecified type. This matching determines the external space to be of Schwarzschild type. By this, it is also possi- ble to determine that the constant of integration that appears in the Newtonian Cosmology, coincides with the spatial curvature of the FLRW metric. All we assumed was some classical boundary conditions and basic assumptions.
- Aug 22 2017 cs.RO arXiv:1708.06343v1
- Aug 22 2017 hep-th arXiv:1708.06342v1
- Aug 22 2017 math.AG arXiv:1708.06340v1
- Aug 22 2017 hep-th arXiv:1708.06339v1
- Aug 22 2017 stat.ME arXiv:1708.06337v1
- Aug 22 2017 cond-mat.str-el arXiv:1708.06335v1
- Aug 22 2017 cond-mat.mes-hall physics.app-ph arXiv:1708.06331v1
- Aug 22 2017 physics.optics physics.class-ph arXiv:1708.06330v1
- Aug 22 2017 math.AP arXiv:1708.06329v1
- Aug 22 2017 hep-th arXiv:1708.06328v1
- Aug 22 2017 hep-th arXiv:1708.06327v1
- Aug 22 2017 hep-ph arXiv:1708.06326v1
- Aug 22 2017 math.AG arXiv:1708.06325v1
- Aug 22 2017 nucl-th arXiv:1708.06321v1
- Aug 22 2017 cs.CV arXiv:1708.06320v1
- Aug 22 2017 math.DG arXiv:1708.06316v1
- Aug 22 2017 physics.flu-dyn astro-ph.EP arXiv:1708.06314v1
- Aug 22 2017 cs.NI arXiv:1708.06313v1
- Aug 22 2017 cs.LO arXiv:1708.06312v1
- Aug 22 2017 physics.ins-det arXiv:1708.06311v1
- Aug 22 2017 cs.SI arXiv:1708.06309v1
- Aug 22 2017 cs.CR arXiv:1708.06308v1
- Aug 22 2017 math.AP arXiv:1708.06307v1
- Aug 22 2017 math.NA arXiv:1708.06306v1