Unbounded sequence of observers exhibiting Einstein-Podolsky-Rosen steering

A sequential steering scenario is investigated, where multiple Bobs aim at demonstrating steering using successively the same half of an entangled quantum state. With isotropic entangled states of local dimension $d$, the number of Bobs that can steer Alice is found to be $N_\mathrm{Bob}\sim d/\log{d}$, thus leading to an arbitrary large number of successive instances of steering with independently chosen and unbiased inputs. This scaling is achieved when considering a general class of measurements along orthonormal bases, as well as complete sets of mutually unbiased bases. Finally, we show that similar results can be obtained in an anonymous sequential scenario, where none of the Bobs know their position in the sequence.Comment: 7 pages, 4 figure

The practice of going helps children to stop:The importance of context monitoring in inhibitory control

How do we stop ourselves during ongoing action? Recent work implies that stopping per se is easy given sufficient monitoring of contextual cues signaling the need to change action. We test key implications of this idea for improving inhibitory control. Seven- to 9-year old children practiced stopping an ongoing action, or monitoring for cues that signaled the need to go again. Both groups subsequently showed better response inhibition in a Stop-Signal task than active controls, and practice monitoring yielded a dose-response relationship. When monitoring practice was optimized to occur while children engaged in responding, the greatest benefits were observed – even greater than from practicing stopping itself. These findings demonstrate the importance of monitoring processes in developing response inhibition, and suggest promising new directions for interventions

Depinning of disordered bosonic chains

We consider one-dimensional bosonic chains with a repulsive boson-boson interaction that decays exponentially on large length-scales. This model describes transport of Cooper-pairs in a Josepshon junction array, or transport of magnetic flux quanta in quantum-phase-slip ladders, i.e. arrays of superconducting wires in a ladder-configuration that allow for the coherent tunnelling of flux quanta. In the low-frequency, long wave-length regime these chains can be mapped to an effective model of a one-dimensional elastic field in a disordered potential. The onset of transport in these systems, when biased by external voltage, is described by the standard depinning theory of elastic media in disordered pinning potentials. We numerically study the regimes that are of relevance for quantum-phase-slip ladders. These are (i) very short chains and (ii) the regime of weak disorder. For chains shorter than the typical pinning length, i.e., the Larkin length, the chains reach a saturation regime where the depinning voltage does not depend on the decay length of the repulsive interaction. In the regime of weak disorder we find an emergent correlation length-scale that depends on the disorder strength. For arrays shorter than this length the onset of transport is similar to the clean arrays, i.e., is due to the penetration of solitons into the array. We discuss the depinning scenarios for longer arrays in this regime.Comment: 11 pages, 6 figure

Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition

We address the breakdown of the bulk-boundary correspondence observed in non-Hermitian systems, where open and periodic systems can have distinct phase diagrams. The correspondence can be completely restored by considering the Hamiltonian's singular value decomposition instead of its eigendecomposition. This leads to a natural topological description in terms of a flattened singular decomposition. This description is equivalent to the usual approach for Hermitian systems and coincides with a recent proposal for the classification of non-Hermitian systems. We generalize the notion of the entanglement spectrum to non-Hermitian systems, and show that the edge physics is indeed completely captured by the periodic bulk Hamiltonian. We exemplify our approach by considering the chiral non-Hermitian Su-Schrieffer-Heger and Chern insulator models. Our work advocates a different perspective on topological non-Hermitian Hamiltonians, paving the way to a better understanding of their entanglement structure.Comment: 6+5 pages, 8 figure

Investigating dynamic dependence using copulae

A general methodology for time series modelling is developed which works down from distributional properties to implied structural models including the standard regression relationship. This general to specific approach is important since it can avoid spurious assumptions such as linearity in the form of the dynamic relationship between variables. It is based on splitting the multivariate distribution of a time series into two parts: (i) the marginal unconditional distribution, (ii) the serial dependence encompassed in a general function , the copula. General properties of the class of copula functions that fulfill the necessary requirements for Markov chain construction are exposed. Special cases for the gaussian copula with AR(p) dependence structure and for archimedean copulae are presented. We also develop copula based dynamic dependency measures — auto-concordance in place of autocorrelation. Finally, we provide empirical applications using financial returns and transactions based forex data. Our model encompasses the AR(p) model and allows non-linearity. Moreover, we introduce non-linear time dependence functions that generalize the autocorrelation function