Naturally reductive pseudo-Riemannian spaces

A family of naturally reductive pseudo-Riemannian spaces is constructed out of the representations of Lie algebras with ad-invariant metrics. We exhibit peculiar examples, study their geometry and characterize the corresponding naturally reductive homogeneous structure.Comment: A shorter, clearer and more concise versio

Symptom-severity-related brain connectivity alterations in functional movement disorders

Background Functional movement disorders, a common cause of neurological disabilities, can occur with heterogeneous motor manifestations including functional weakness. However, the underlying mechanisms related to brain function and connectivity are unknown. Objective To identify brain connectivity alterations related to functional weakness we assessed network centrality changes in a group of patients with heterogeneous motor manifestations using task-free functional MRI in combination with different network centrality approaches. Methods Task-free functional MRI was performed in 48 patients with heterogeneous motor manifestations including 28 patients showing functional weakness and 65 age- and sex-matched healthy controls. Functional connectivity differences were assessed using different network centrality approaches, i.e. global correlation, eigenvector centrality, and intrinsic connectivity. Motor symptom severity was assessed using The Simplified Functional Movement Disorders Rating Scale and correlated with network centrality. Results Comparing patients with and without functional weakness showed significant network centrality differences in the left temporoparietal junction and precuneus. Patients with functional weakness showed increased centrality in the same anatomical regions when comparing functional weakness with healthy controls. Moreover, in the same regions, patients with functional weakness showed a positive correlation between motor symptom severity and network centrality. This correlation was shown to be specific to functional weakness with an interaction analysis, confirming a significant difference between patients with and without functional weakness. Conclusions We identified the temporoparietal junction and precuneus as key regions involved in brain connectivity alterations related to functional weakness. We propose that both regions may be promising targets for phenotype-specific non-invasive brain stimulation

Experimental asymmetric phase-covariant quantum cloning of polarization qubits

We report on two optical realizations of the $1 \to 2$ asymmetric phase-covariant cloning machines for polarization states of single photons. The experimental setups combine two-photon interference and tunable polarization filtering that enables us to control the asymmetry of the cloners. The first scheme involves a special unbalanced bulk beam splitter exhibiting different splitting ratios for vertical and horizontal polarizations, respectively. The second implemented scheme consists of a balanced fiber coupler where photon bunching occurs, followed by a free-space part with polarization filters. With this later approach we were able to demonstrate very high cloning fidelities which are above the universal cloning limit.Comment: 7 pages, 8 figure

Unambiguous state discrimination in quantum cryptography with weak coherent states

The use of linearly independent signal states in realistic implementations of quantum key distribution (QKD) enables an eavesdropper to perform unambiguous state discrimination. We explore quantitatively the limits for secure QKD imposed by this fact taking into account that the receiver can monitor to some extend the photon number statistics of the signals even with todays standard detection schemes. We compare our attack to the beamsplitting attack and show that security against beamsplitting attack does not necessarily imply security against the attack considered here.Comment: 10 pages, 6 figures, updated version with added discussion of beamsplitting attac

Abnormal activity in the precuneus during time perception in Parkinson’s disease: An fMRI study

Background Parkinson's disease (PD) patients are deficient in time estimation. This deficit improves after dopamine (DA) treatment and it has been associated with decreased internal timekeeper speed, disruption of executive function and memory retrieval dysfunction. Methodology/Findings The aim of the present study was to explore the neurophysiologic correlates of this deficit. We performed functional magnetic resonance imaging on twelve PD patients while they were performing a time reproduction task (TRT). The TRT consisted of an encoding phase (during which visual stimuli of durations from 5s to 16.6s, varied at 8 levels were presented) and a reproduction phase (during which interval durations were reproduced by a button pressing). Patients were scanned twice, once while on their DA medication (ON condition) and once after medication withdrawal (OFF condition). Differences in Blood-Oxygenation-Level-Dependent (BOLD) signal in ON and OFF conditions were evaluated. The time course of activation in the brain areas with different BOLD signal was plotted. There were no significant differences in the behavioral results, but a trend toward overestimation of intervals ≤11.9s and underestimation of intervals ≥14.1s in the OFF condition (p<0.088). During the reproduction phase, higher activation in the precuneus was found in the ON condition (p<0.05 corrected). Time course was plotted separately for long (≥14.1s) and short (≤11.9s) intervals. Results showed that there was a significant difference only in long intervals, when activity gradually decreased in the OFF, but remained stable in the ON condition. This difference in precuneus activation was not found during random button presses in a control task. Conclusions/Significance Our results show that differences in precuneus activation during retrieval of a remembered duration may underlie some aspects of time perception deficit in PD patients. We suggest that DA medication may allow compensatory activation in the precuneus, which results in a more accurate retrieval of remembered interval duration

Homogeneous geodesics of non-unimodular Lorentzian Lie groups and naturally reductive Lorentzian spaces in dimension three

We determine, for all three-dimensional non-unimodular Lie groups equipped with a Lorentzian metric, the set of homogeneous geodesics through a point. Together with the results of [C] and [CM2], this leads to the full classification of three-dimensional Lorentzian g.o. spaces and naturally reductive spaces

The Security of Practical Quantum Key Distribution

Quantum key distribution (QKD) is the first quantum information task to reach the level of mature technology, already fit for commercialization. It aims at the creation of a secret key between authorized partners connected by a quantum channel and a classical authenticated channel. The security of the key can in principle be guaranteed without putting any restriction on the eavesdropper's power. The first two sections provide a concise up-to-date review of QKD, biased toward the practical side. The rest of the paper presents the essential theoretical tools that have been developed to assess the security of the main experimental platforms (discrete variables, continuous variables and distributed-phase-reference protocols).Comment: Identical to the published version, up to cosmetic editorial change

Security against individual attacks for realistic quantum key distribution

I prove the security of quantum key distribution against individual attacks for realistic signals sources, including weak coherent pulses and downconversion sources. The proof applies to the BB84 protocol with the standard detection scheme (no strong reference pulse). I obtain a formula for the secure bit rate per time slot of an experimental setup which can be used to optimize the performance of existing schemes for the considered scenario.Comment: 10 pages, 4 figure