A min-entropy uncertainty relation for finite size cryptography

Apart from their foundational significance, entropic uncertainty relations play a central role in proving the security of quantum cryptographic protocols. Of particular interest are thereby relations in terms of the smooth min-entropy for BB84 and six-state encodings. Previously, strong uncertainty relations were obtained which are valid in the limit of large block lengths. Here, we prove a new uncertainty relation in terms of the smooth min-entropy that is only marginally less strong, but has the crucial property that it can be applied to rather small block lengths. This paves the way for a practical implementation of many cryptographic protocols. As part of our proof we show tight uncertainty relations for a family of Renyi entropies that may be of independent interest.Comment: 5+6 pages, 1 figure, revtex. new version changed author's name from Huei Ying Nelly Ng to Nelly Huei Ying Ng, for consistency with other publication

Disentanglement cost of quantum states.

We show that the minimal rate of noise needed to catalytically erase the entanglement in a bipartite quantum state is given by the regularized relative entropy of entanglement. This offers a solution to the central open question raised in [Groisman et al., Phys. Rev. A 72, 032317 (2005)PLRAAN1050-294710.1103/PhysRevA.72.032317] and complements their main result that the minimal rate of noise needed to erase all correlations is given by the quantum mutual information. We extend our discussion to the tripartite setting where we show that an asymptotic rate of noise given by the regularized relative entropy of recovery is sufficient to catalytically transform the state to a locally recoverable version of the state

Conditional decoupling of quantum information

Insights from quantum information theory show that correlation measures based on quantum entropy are fundamental tools that reveal the entanglement structure of multipartite states. In that spirit, Groisman, Popescu, and Winter [Phys. Rev. A 72, 032317 (2005)PLRAAN1050-294710.1103/PhysRevA.72.032317] showed that the quantum mutual information I(A;B) quantifies the minimal rate of noise needed to erase the correlations in a bipartite state of quantum systems AB. Here, we investigate correlations in tripartite systems ABE. In particular, we are interested in the minimal rate of noise needed to apply to the systems AE in order to erase the correlations between A and B given the information in system E, in such a way that there is only negligible disturbance on the marginal BE. We present two such models of conditional decoupling, called deconstruction and conditional erasure cost of tripartite states ABE. Our main result is that both are equal to the conditional quantum mutual information I(A;B|E) - establishing it as an operational measure for tripartite quantum correlations

Quasi-polynomial time algorithms for free quantum games in bounded dimension

We give a converging semidefinite programming hierarchy of outer approximations for the set of quantum correlations of fixed dimension and derive analytical bounds on the convergence speed of the hierarchy. In particular, we give a semidefinite program of size $\exp(\mathcal{O}\big(T^{12}(\log^2(AT)+\log(Q)\log(AT))/\epsilon^2\big))$ to compute additive $\epsilon$-approximations on the values of two-player free games with $T\times T$-dimensional quantum assistance, where $A$ and $Q$ denote the numbers of answers and questions of the game, respectively. For fixed dimension $T$, this scales polynomially in $Q$ and quasi-polynomially in $A$, thereby improving on previously known approximation algorithms for which worst-case run-time guarantees are at best exponential in $Q$ and $A$. For the proof, we make a connection to the quantum separability problem and employ improved multipartite quantum de Finetti theorems with linear constraints. We also derive an informationally complete measurement which minimises the loss in distinguishability relative to the quantum side information - which may be of independent interest

The XMM-Newton survey of the ELAIS-S1 field II: optical identifications and multiwavelength catalogue of X-ray sources

We present optical identifications and a multi-band catalogue of a sample of 478 X-ray sources in the XMM and Chandra surveys of the central 0.6 deg^2 of the ELAIS-S1 field. The optical/infrared counterpart of each X-ray source was identified using R and IRAC 3.6 um bands. This method was complemented by the precise positions obtained through Chandra observations. Approximately 94% of the counterparts are detected in the R band, while the remaining are blank fields in the optical down to R~24.5, but have a near-infrared counterpart detected by IRAC within 6 arcsec from the XMM centroid. The multi-band catalogue contains photometry in ten photometric bands (B to the MIPS 24 um). We determined redshift and classification for 237 sources (~50% of the sample) brighter than R=24. We classified 47% of the sources with spectroscopic redshift as broad-line active galactic nuclei (BL AGNs) with z=0.1-3.5, while sources without broad-lines are about 46% of the spectroscopic sample and are found up to z=2.6. We identified 11 type 2 QSOs among the sources with X/O>8, with z=0.9-2.6, high 2-10 keV luminosity (log(L2-10keV)>=43.8 erg/s) and hard X-ray colors suggesting large absorbing columns at the rest frame (logN_H up to 23.6 cm^-2). BL AGNs show on average blue optical-to-near-infrared colors, softer X-ray colors and X-ray-to-optical colors typical of optically selected AGNs. Conversely, narrow-line sources show redder optical colors, harder X-ray flux ratio and span a wider range of X-ray-to-optical colors. On average the SEDs of high-luminosity BL AGNs resemble the power-law typical of unobscured AGNs. The SEDs of NOT BL AGNs are dominated by the galaxy emission in the optical/near-infrared, and show a rise in the mid-infrared which suggests the presence of an obscured active nucleus.Comment: 15 pages, A&A accepted, affiliations correcte

Incidence of psychotic disorders and its association with methodological issues. A systematic review and meta-analyses.

In the current study, we aimed to determine if the variability of the incidence rates of psychosis found was associated with methodo-logical aspect of the studies such as: study type, case ascertainment, diagnosis, diagnostic instrument to confirm cases, diagnostic classification system, duration of the case ascertainment, lower and upper age included in the studies and quality of the study.A meta-analysis of these factors was performed for all incidence rates as a whole. For the analysis of subgroups we used a mixed effects model. For each subgroup, heterogeneity was calculated using the Q sta- tistic and its corresponding p-value. In addition, a multivariate regression was performed. We analysed 92 estimates of incidence of psychosis corresponding to 30 citations from our previous meta-analysis. The pooled incidence rates of psychosis (mean effect: 18.30 per 100,000 [14.19–22.42]) revealed that heterogeneity between studies was very high. The final model explains 63.53% of the variability in the incidence rates reported by the different studies. Based on the subgroup analysis, we found statistically significant differences in incidence rates associated with diagnosis, diagnostic instruments used, duration of case ascertainment period and ages of both lower and upper cutoff. Finally, study type and quality of the studies had a weak association.Regarding meta-regression, studies that collected patients in the first contact with mental health units presented higher incidences rated, but with a weak association, more cases are detected in the studies in which the cases are included at the first contact, since there is not always an admission in the first episode. Studies that recruited patients in mental health units and primary care services, or in both and in social services had significantly higher incidence rates than only in primary care