Entanglement in the quantum Ising model

We study the asymptotic scaling of the entanglement of a block of spins for the ground state of the one-dimensional quantum Ising model with transverse field. When the field is sufficiently strong, the entanglement grows at most logarithmically in the number of spins. The proof utilises a transformation to a model of classical probability called the continuum random-cluster model, and is based on a property of the latter model termed ratio weak-mixing. Our proof applies equally to a large class of disordered interactions

Gaussian quantum marginal problem

The quantum marginal problem asks what local spectra are consistent with a given spectrum of a joint state of a composite quantum system. This setting, also referred to as the question of the compatibility of local spectra, has several applications in quantum information theory. Here, we introduce the analogue of this statement for Gaussian states for any number of modes, and solve it in generality, for pure and mixed states, both concerning necessary and sufficient conditions. Formally, our result can be viewed as an analogue of the Sing-Thompson Theorem (respectively Horn's Lemma), characterizing the relationship between main diagonal elements and singular values of a complex matrix: We find necessary and sufficient conditions for vectors (d1, ..., dn) and (c1, ..., cn) to be the symplectic eigenvalues and symplectic main diagonal elements of a strictly positive real matrix, respectively. More physically speaking, this result determines what local temperatures or entropies are consistent with a pure or mixed Gaussian state of several modes. We find that this result implies a solution to the problem of sharing of entanglement in pure Gaussian states and allows for estimating the global entropy of non-Gaussian states based on local measurements. Implications to the actual preparation of multi-mode continuous-variable entangled states are discussed. We compare the findings with the marginal problem for qubits, the solution of which for pure states has a strikingly similar and in fact simple form.Comment: 18 pages, 1 figure, material added, references updated, except from figure identical with version to appear in Commun. Math. Phy

Planck intermediate results. VIII. Filaments between interacting clusters

About half of the baryons of the Universe are expected to be in the form of filaments of hot and low density intergalactic medium. Most of these baryons remain undetected even by the most advanced X-ray observatories which are limited in sensitivity to the diffuse low density medium. The Planck satellite has provided hundreds of detections of the hot gas in clusters of galaxies via the thermal Sunyaev-Zel'dovich (tSZ) effect and is an ideal instrument for studying extended low density media through the tSZ effect. In this paper we use the Planck data to search for signatures of a fraction of these missing baryons between pairs of galaxy clusters. Cluster pairs are good candidates for searching for the hotter and denser phase of the intergalactic medium (which is more easily observed through the SZ effect). Using an X-ray catalogue of clusters and the Planck data, we select physical pairs of clusters as candidates. Using the Planck data we construct a local map of the tSZ effect centered on each pair of galaxy clusters. ROSAT data is used to construct X-ray maps of these pairs. After having modelled and subtracted the tSZ effect and X-ray emission for each cluster in the pair we study the residuals on both the SZ and X-ray maps. For the merging cluster pair A399-A401 we observe a significant tSZ effect signal in the intercluster region beyond the virial radii of the clusters. A joint X-ray SZ analysis allows us to constrain the temperature and density of this intercluster medium. We obtain a temperature of kT = 7.1 +- 0.9, keV (consistent with previous estimates) and a baryon density of (3.7 +- 0.2)x10^-4, cm^-3. The Planck satellite mission has provided the first SZ detection of the hot and diffuse intercluster gas.Comment: Accepted by A&

Planck early results. IX. XMM-Newton follow-up for validation of Planck cluster candidates

We present the XMM-Newton follow-up for confirmation of Planck cluster candidates. Twenty-five candidates have been observed to date using snapshot (∼10 ks) exposures, ten as part of a pilot programme to sample a low range of signal-to-noise ratios (4 < S/N < 6), and a further 15 in a programme to observe a sample of S/N > 5 candidates. The sensitivity and spatial resolution of XMM-Newton allows unambiguous discrimination between clusters and false candidates. The 4 false candidates have S/N ≤ 4.1. A total of 21 candidates are confirmed as extended X-ray sources. Seventeen are single clusters, the majority of which are found to have highly irregular and disturbed morphologies (about ∼70%). The remaining four sources are multiple systems, including the unexpected discovery of a supercluster at z = 0.45. For 20 sources we are able to derive a redshift estimate from the X-ray Fe K line (albeit of variable quality). The new clusters span the redshift range 0.09 <∼ z <∼ 0.54, with a median redshift of z ∼ 0.37. A first determination is made of their X-ray properties including the characteristic size, which is used to improve the estimate of the SZ Compton parameter, Y500. The follow-up validation programme has helped to optimise the Planck candidate selection process. It has also provided a preview of the X-ray properties of these newly-discovered clusters, allowing comparison with their SZ properties, and to the X-ray and SZ properties of known clusters observed in the Planck survey. Our results suggest that Planck may have started to reveal a non-negligible population of massive dynamically perturbed objects that is under-represented in X-ray surveys. However, despite their particular properties, these new clusters appear to follow the Y500–YX relation established for X-ray selected objects, where YX is the product of the gas mass and temperature

Planck early results. II. The thermal performance of Planck

The performance of the Planck instruments in space is enabled by their low operating temperatures, 20 K for LFI and 0.1 K for HFI, achieved through a combination of passive radiative cooling and three active mechanical coolers. The scientific requirement for very broad frequency coverage led to two detector technologies with widely different temperature and cooling needs. Active coolers could satisfy these needs; a helium cryostat, as used by previous cryogenic space missions (IRAS, COBE, ISO, Spitzer, AKARI), could not. Radiative cooling is provided by three V-groove radiators and a large telescope baffle. The active coolers are a hydrogen sorption cooler (<20 K), a 4He Joule-Thomson cooler (4.7 K), and a 3He-4He dilution cooler (1.4 K and 0.1 K). The flight system was at ambient temperature at launch and cooled in space to operating conditions. The HFI bolometer plate reached 93 mK on 3 July 2009, 50 days after launch. The solar panel always faces the Sun, shadowing the rest of Planck, and operates at a mean temperature of 384 K. At the other end of the spacecraft, the telescope baffle operates at 42.3 K and the telescope primary mirror operates at 35.9 K. The temperatures of key parts of the instruments are stabilized by both active and passive methods. Temperature fluctuations are driven by changes in the distance from the Sun, sorption cooler cycling and fluctuations in gas-liquid flow, and fluctuations in cosmic ray flux on the dilution and bolometer plates. These fluctuations do not compromise the science data

Planck Early Results. VII. The Early Release Compact Source Catalogue

A brief description of the methodology of construction, contents and usage of the Planck Early Release Compact Source Catalogue (ERCSC), including the Early Cold Cores (ECC) and the Early Sunyaev-Zeldovich (ESZ) cluster catalogue is provided. The catalogue is based on data that consist of mapping the entire sky once and 60% of the sky a second time by Planck, thereby comprising the first high sensitivity radio/submillimetre observations of the entire sky. Four source detection algorithms were run as part of the ERCSC pipeline. A Monte-Carlo algorithm based on the injection and extraction of artificial sources into the Planck maps was implemented to select reliable sources among all extracted candidates such that the cumulative reliability of the catalogue is ≥90%. There is no requirement on completeness for the ERCSC. As a result of the Monte-Carlo assessment of reliability of sources from the different techniques, an implementation of the PowellSnakes source extraction technique was used at the five frequencies between 30 and 143 GHz while the SExtractor technique was used between 217 and 857GHz. The 10σ photometric flux density limit of the catalogue at |b| > 30◦ is 0.49, 1.0, 0.67, 0.5, 0.33, 0.28, 0.25, 0.47 and 0.82 Jy at each of the nine frequencies between 30 and 857 GHz. Sources which are up to a factor of ∼2 fainter than this limit, and which are present in “clean” regions of the Galaxy where the sky background due to emission from the interstellar medium is low, are included in the ERCSC if they meet the high reliability criterion. The Planck ERCSC sources have known associations to stars with dust shells, stellar cores, radio galaxies, blazars, infrared luminous galaxies and Galactic interstellar medium features. A significant fraction of unclassified sources are also present in the catalogs. In addition, two early release catalogs that contain 915 cold molecular cloud core candidates and 189 SZ cluster candidates that have been generated using multifrequency algorithms are presented. The entire source list, with more than 15000 unique sources, is ripe for follow-up characterisation with Herschel, ATCA, VLA, SOFIA, ALMA and other ground-based observing facilities

Planck early results IX : XMM-Newton follow-up for validation of Planck cluster candidates

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