A volume inequality for quantum Fisher information and the uncertainty principle

Let $A_1,...,A_N$ be complex self-adjoint matrices and let $\rho$ be a density matrix. The Robertson uncertainty principle $$det(Cov_\rho(A_h,A_j)) \geq det(- \frac{i}{2} Tr(\rho [A_h,A_j]))$$ gives a bound for the quantum generalized covariance in terms of the commutators $[A_h,A_j]$. The right side matrix is antisymmetric and therefore the bound is trivial (equal to zero) in the odd case $N=2m+1$. Let $f$ be an arbitrary normalized symmetric operator monotone function and let $_{\rho,f}$ be the associated quantum Fisher information. In this paper we conjecture the inequality $$det (Cov_\rho(A_h,A_j)) \geq det (\frac{f(0)}{2} _{\rho,f})$$ that gives a non-trivial bound for any natural number $N$ using the commutators $i[\rho, A_h]$. The inequality has been proved in the cases $N=1,2$ by the joint efforts of many authors. In this paper we prove the case N=3 for real matrices

Diversity and Adaptation in Large Population Games

We consider a version of large population games whose players compete for resources using strategies with adaptable preferences. The system efficiency is measured by the variance of the decisions. In the regime where the system can be plagued by the maladaptive behavior of the players, we find that diversity among the players improves the system efficiency, though it slows the convergence to the steady state. Diversity causes a mild spread of resources at the transient state, but reduces the uneven distribution of resources in the steady state.Comment: 8 pages, 3 figure

Metric adjusted skew information: Convexity and restricted forms of superadditivity

We give a truly elementary proof of the convexity of metric adjusted skew information following an idea of Effros. We extend earlier results of weak forms of superadditivity to general metric adjusted skew informations. Recently, Luo and Zhang introduced the notion of semi-quantum states on a bipartite system and proved superadditivity of the Wigner-Yanase-Dyson skew informations for such states. We extend this result to general metric adjusted skew informations. We finally show that a recently introduced extension to parameter values $1<p\le 2$ of the WYD-information is a special case of (unbounded) metric adjusted skew information.Comment: An error in the literature is pointed ou

Information geometry of density matrices and state estimation

Given a pure state vector |x> and a density matrix rho, the function p(x|rho)= defines a probability density on the space of pure states parameterised by density matrices. The associated Fisher-Rao information measure is used to define a unitary invariant Riemannian metric on the space of density matrices. An alternative derivation of the metric, based on square-root density matrices and trace norms, is provided. This is applied to the problem of quantum-state estimation. In the simplest case of unitary parameter estimation, new higher-order corrections to the uncertainty relations, applicable to general mixed states, are derived.Comment: published versio

Stereoisomer libraries: Total synthesis of all 16 stereoisomers of the pine sawfly sex pheromone by a fluorous mixture-synthesis approach

All 16 stereoisomers of the sex pheromone of pine sawfly (3,7,11-trimethylundecanol propanoate ester) have been synthesized on a 10- to 20-mg scale by a split-parallel fluorous mixture-synthesis approach. Spectral data obtained for all 32 compounds (16 alcohols and the corresponding propionates) matched well with published data, thereby validating the fluorous-tag encoding of diastereoisomers. This fluorous-tag encoding method is recommended for the efficient synthesis of multiple stereoisomers for spectroscopic studies, biological tests, or other structure-function relationships

SED-inferred properties and morphology of Lyman-break galaxies at z∼1z\sim 1 in the CDF-S

After carefully cross-identifying a previously discovered GALEX-selected Lyman Break Galaxy (LBG) candidates one-to-one with their optical counterparts in the field of the CDF-S, we re-estimate their photometric redshifts using multi-wavelength data from UV, optical to NIR. We refine a new updated sample of 383 LBGs at 0.7\la z \la 1.4. Most LBGs are classified as starburst and irregular types. Ages spread from several Myr to 1.5Gyr. Their dust-corrected star formation rates (SFRs) and stellar masses ($M_*$) are from 4\my to 220\my and from 2.3\times 10^8 \msun to 4 \times 10^{11} \msun. The rest-frame FUV luminosity function of LBGs are presented. LBGs of irregular types mainly distribute along the "main sequence" of star forming galaxies while most LBGs of starburst types locate in the starburst region. A "downsizing" effect is clearly found and LBGs distribute in the "blue" cloud. HST images in F606W ($V$ band) and F850LP ($z$ band) are taken from the GEMS and GOODS-S surveys. SExtractor and GALFIT are applied to get their morphological parameters. A morphological sample of 142 LBGs with reliable results of \sersic and sizes in both bands is defined. We find that LBGs at $z\sim 1$ are dominated by disk-like galaxies. Correlations between photometric and morphological properties of LBGs are investigated. Strong correlations between their half-light radii and $M_*$, i.e., size-stellar mass relations, are found in both bands. Physical connections between correlations and the "downsizing" effect are discussed.Comment: 26 pages, 30 figures, 6 tables, accepted by MNRA