Improving the precision matrix for precision cosmology

The estimation of cosmological constraints from observations of the large scale structure of the Universe, such as the power spectrum or the correlation function, requires the knowledge of the inverse of the associated covariance matrix, namely the precision matrix, $\mathbf{\Psi}$. In most analyses, $\mathbf{\Psi}$ is estimated from a limited set of mock catalogues. Depending on how many mocks are used, this estimation has an associated error which must be propagated into the final cosmological constraints. For future surveys such as Euclid and DESI, the control of this additional uncertainty requires a prohibitively large number of mock catalogues. In this work we test a novel technique for the estimation of the precision matrix, the covariance tapering method, in the context of baryon acoustic oscillation measurements. Even though this technique was originally devised as a way to speed up maximum likelihood estimations, our results show that it also reduces the impact of noisy precision matrix estimates on the derived confidence intervals, without introducing biases on the target parameters. The application of this technique can help future surveys to reach their true constraining power using a significantly smaller number of mock catalogues.Comment: 9 pages, 7 figures, minor changes to match version accepted by MNRA

Measuring work and heat in ultracold quantum gases

We propose a feasible experimental scheme to direct measure heat and work in cold atomic setups. The method is based on a recent proposal which shows that work is a positive operator valued measure (POVM). In the present contribution, we demonstrate that the interaction between the atoms and the light polarisation of a probe laser allows us to implement such POVM. In this way the work done on or extracted from the atoms after a given process is encoded in the light quadrature that can be measured with a standard homodyne detection. The protocol allows one to verify fluctuation theorems and study properties of the non-unitary dynamics of a given thermodynamic process.Comment: Published version in the Focus Issue on "Quantum Thermodynamics

Communicating via ignorance: Increasing communication capacity via superposition of order

Classically, no information can be transmitted through a depolarising, that is a completely noisy, channel. We show that by combining a depolarising channel with another channel in an indefinite causal order---that is, when there is superposition of the order that these two channels were applied---it becomes possible to transmit significant information. We consider two limiting cases. When both channels are fully-depolarising, the ideal limit is communication of 0.049 bits; experimentally we achieve $(3.4{\pm}0.2){\times}10^{-2}$ bits. When one channel is fully-depolarising, and the other is a known unitary, the ideal limit is communication of 1 bit. We experimentally achieve 0.64${\pm}$0.02 bits. Our results offer intriguing possibilities for future communication strategies beyond conventional quantum Shannon theory

Shapes of clusters and groups of galaxies: Comparison of model predictions with observations

We study the properties of the 3-dimensional and projected shapes of haloes using high resolution numerical simulations and observational data where the latter comes from the 2PIGG (Eke et al. 2004) and SDSS-DR3GC group catalogues (Merchan & Zandivarez 2005). We investigate the dependence of halo shape on characteristics such as mass and number of members. In the 3-dimensional case, we find a significant correlation between the mass and halo shape; massive systems are more prolate than small haloes. We detect a source of strong systematics in estimates of the triaxiality of a halo, which is found to be a strong function of the number of members; LCDM haloes usually characterised by triaxial shapes, slightly bent toward prolate forms, appear more oblate when taking only a small subset of the halo particles. The ellipticities of observed 2PIGG and SDSS-DR3GC groups are found to be strongly dependent on the number of group members, so that poor groups appear more elongated than rich ones. However, this is again an artifact caused by poor statistics and not an intrinsic property of the galaxy groups, nor an effect from observational biases. We interpret these results with the aid of a GALFORM mock 2PIGG catalogue. When comparing the group ellipticities in mock and real catalogues, we find an excellent agreement between the trends of shapes with number of group members. When carefully taking into account the effects of low number statistics, we find that more massive groups are consistent with more elongated shapes. Finally, our studies find no significant correlations between the shape of observed 2PIGG or SDSS-DR3GC groups with the properties of galaxy members such as colour or spectral type index.Comment: 9 pages, 10 figures, submitted to MNRA