Explicit lower and upper bounds on the entangled value of multiplayer XOR games

XOR games are the simplest model in which the nonlocal properties of entanglement manifest themselves. When there are two players, it is well known that the bias --- the maximum advantage over random play --- of entangled players can be at most a constant times greater than that of classical players. Recently, P\'{e}rez-Garc\'{i}a et al. [Comm. Math. Phys. 279 (2), 2008] showed that no such bound holds when there are three or more players: the advantage of entangled players over classical players can become unbounded, and scale with the number of questions in the game. Their proof relies on non-trivial results from operator space theory, and gives a non-explicit existence proof, leading to a game with a very large number of questions and only a loose control over the local dimension of the players' shared entanglement. We give a new, simple and explicit (though still probabilistic) construction of a family of three-player XOR games which achieve a large quantum-classical gap (QC-gap). This QC-gap is exponentially larger than the one given by P\'{e}rez-Garc\'{i}a et. al. in terms of the size of the game, achieving a QC-gap of order $\sqrt{N}$ with $N^2$ questions per player. In terms of the dimension of the entangled state required, we achieve the same (optimal) QC-gap of $\sqrt{N}$ for a state of local dimension $N$ per player. Moreover, the optimal entangled strategy is very simple, involving observables defined by tensor products of the Pauli matrices. Additionally, we give the first upper bound on the maximal QC-gap in terms of the number of questions per player, showing that our construction is only quadratically off in that respect. Our results rely on probabilistic estimates on the norm of random matrices and higher-order tensors which may be of independent interest.Comment: Major improvements in presentation; results identica

Large violation of Bell inequalities with low entanglement

In this paper we obtain violations of general bipartite Bell inequalities of order $\frac{\sqrt{n}}{\log n}$ with $n$ inputs, $n$ outputs and $n$-dimensional Hilbert spaces. Moreover, we construct explicitly, up to a random choice of signs, all the elements involved in such violations: the coefficients of the Bell inequalities, POVMs measurements and quantum states. Analyzing this construction we find that, even though entanglement is necessary to obtain violation of Bell inequalities, the Entropy of entanglement of the underlying state is essentially irrelevant in obtaining large violation. We also indicate why the maximally entangled state is a rather poor candidate in producing large violations with arbitrary coefficients. However, we also show that for Bell inequalities with positive coefficients (in particular, games) the maximally entangled state achieves the largest violation up to a logarithmic factor.Comment: Reference [16] added. Some typos correcte

Huntington's disease cerebrospinal fluid seeds aggregation of mutant huntingtin

Huntington's disease (HD), a progressive neurodegenerative disease, is caused by an expanded CAG triplet repeat producing a mutant huntingtin protein (mHTT) with a polyglutamine-repeat expansion. Onset of symptoms in mutant huntingtin gene-carrying individuals remains unpredictable. We report that synthetic polyglutamine oligomers and cerebrospinal fluid (CSF) from BACHD transgenic rats and from human HD subjects can seed mutant huntingtin aggregation in a cell model and its cell lysate. Our studies demonstrate that seeding requires the mutant huntingtin template and may reflect an underlying prion-like protein propagation mechanism. Light and cryo-electron microscopy show that synthetic seeds nucleate and enhance mutant huntingtin aggregation. This seeding assay distinguishes HD subjects from healthy and non-HD dementia controls without overlap (blinded samples). Ultimately, this seeding property in HD patient CSF may form the basis of a molecular biomarker assay to monitor HD and evaluate therapies that target mHTT

Neural networks engaged in milliseconds and seconds time processing: evidence from transcranial magnetic stimulation and patients with cortical or subcortical dysfunction

Here, we review recent transcranial magnetic stimulation studies and investigations in patients with neurological disease such as Parkinson's disease and stroke, showing that the neural processing of time requires the activity of wide range-distributed brain networks. The neural activity of the cerebellum seems most crucial when subjects are required to quickly estimate the passage of brief intervals, and when time is computed in relation to precise salient events. Conversely, the circuits involving the striatum and the substantia nigra projecting to the prefrontal cortex (PFC) are mostly implicated in supra-second time intervals and when time is processed in conjunction with other cognitive functions. A conscious representation of temporal intervals relies on the integrity of the prefrontal and parietal cortices. The role of the PFC becomes predominant when time intervals have to be kept in memory, especially for longer supra-second time intervals, or when the task requires a high cognitive level. We conclude that the contribution of these strongly interconnected anatomical structures in time processing is not fixed, depending not only on the duration of the time interval to be assessed by the brain, but also on the cognitive set, the chosen task and the stimulus modality

Managing juvenile Huntington’s disease

Huntington’s disease (HD) is a well-recognized progressive neurodegenerative disorder that follows an autosomal dominant pattern of inheritance. Onset is insidious and can occur at almost any age, but most commonly the diagnosis is made between the ages of 35 and 55 years. Onset ≤20 years of age is classified as juvenile HD (JHD). This age-based definition is arbitrary but remains convenient. There is overlap between the clinical pathological and genetic features seen in JHD and more traditional adult-onset HD. Nonetheless, the frequent predominance of bradykinesia and dystonia early in the course of the illness, more frequent occurrence of epilepsy and myoclonus, more widespread pathology, and larger genetic lesion means that the distinction is still relevant. In addition, the relative rarity of JHD means that the clinician managing the patient is often doing so for the first time. Management is, at best, symptomatic and supportive with few or no evidence-based guidelines. In this article, the authors will review what is known of the condition and present some suggestions based on their experience

Reader Response: Timing and Impact of Psychiatric, Cognitive, and Motor Abnormalities in Huntington Disease

Neurological Motor Disorder