Schr\"odinger uncertainty relation, Wigner-Yanase-Dyson skew information and metric adjusted correlation measure

In this paper, we give a Schr\"odinger-type uncertainty relation using the Wigner-Yanase-Dyson skew information. In addition, we give Schr\"odinger-type uncertainty relation by use of a two-parameter extended correlation measure. Moreover, we give the further generalization for Schr\"odinger-type uncertainty relation by metric adjusted correlation measure. These results generalize our previous result in [Phys. Rev. A, Vol.82(2010), 034101].Comment: Section 3 was revise

Characterising two-sided quantum correlations beyond entanglement via metric-adjusted f-correlations

We introduce an infinite family of quantifiers of quantum correlations beyond entanglement which vanish on both classical-quantum and quantum-classical states and are in one-to-one correspondence with the metric-adjusted skew informations. The `quantum $f-$correlations' are defined as the maximum metric-adjusted $f-$correlations between pairs of local observables with the same fixed equispaced spectrum. We show that these quantifiers are entanglement monotones when restricted to pure states of qubit-qudit systems. We also evaluate the quantum $f-$correlations in closed form for two-qubit systems and discuss their behaviour under local commutativity preserving channels. We finally provide a physical interpretation for the quantifier corresponding to the average of the Wigner-Yanase-Dyson skew informations.Comment: 20 pages, 1 figure. Published versio

Determining the Continuous Family of Quantum Fisher Information from Linear Response Theory

The quantum Fisher information represents the continuous family of metrics on the space of quantum states and places the fundamental limit on the accuracy of quantum state estimation. We show that the entire family of the quantum Fisher information can be determined from linear response theory through generalized covariances. We derive the generalized fluctuation-dissipation theorem that relates the linear response function to generalized covariances and hence allows us to determine the quantum Fisher information from linear response functions, which is experimentally measurable quantities. As an application, we examine the skew information, which is one of the quantum Fisher information, of a harmonic oscillator in thermal equilibrium, and show that the equality of the skew information-based uncertainty relation holds.Comment: 8 pages, 1 figur

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

A unified approach to Local Quantum Uncertainty and Interferometric Power by Metric Adjusted Skew Information

Local quantum uncertainty and interferometric power have been introduced by Girolami et al. in [1,2] as geometric quantifiers of quantum correlations. The aim of the present paper is to discuss their properties in a unified manner by means of the the metric adjusted skew information defined by Hansen in [3].Comment: submitted to Entrop

A unified approach to local quantum uncertainty and interferometric power by metric adjusted skew information

Local quantum uncertainty and interferometric power were introduced by Girolami et al. as geometric quantifiers of quantum correlations. The aim of the present paper is to discuss their properties in a unified manner by means of the metric adjusted skew information defined by Hansen

The effect of anchoring vignettes on factor structures: Student effort as an example

Anchoring vignettes are used as a methodological technique for removing differential interpretation of response categories (DIRC) from scores on subjective self-report measures (King, Murray, Slomon, & Tandon, 2004). This technique requires participants to read one or more short scenarios, or vignettes, designed to represent various levels of a construct. Vignette ratings are used as an indication of DIRC, which is a source of differential item functioning (DIF). Prior research primarily used indirect methods for evaluating vignette quality. In response, the present set of studies proposes using invariance testing as a more direct evaluation of how the use of anchoring vignettes impacts the presence of DIRC. The effort subscale from the Student Opinion Scale (SOS) is used to demonstrate this set of procedures. It is also argued that DIRC will manifest as non-uniform DIF given that corrections using anchoring vignettes should impact the rank order of cases. In these studies, 819 participants were randomly assigned to either a control group (n = 478) or a group that received vignettes (n = 341) prior to responding to the SOS. Invariance testing was completed in two studies. The first study examined the factor structure between the control group and the vignette group before adjusting scores using the vignettes to determine what effect reading the vignettes may have had on the factor structure. The second study examined the invariance between the control group and the vignette group after score adjustment to determine what effect adjusting scores using the vignettes may have had on the factor structure. Results for the first study supported strict factorial invariance (configural, metric, and scalar invariance, and residuals) and equivalent latent means, which suggests that just viewing the vignettes had insubstantial impact on the factor structure of the SOS effort subscale. Results for the second study also supported strict factorial invariance, but there was a substantial difference in the group’s latent means. This result suggests that DIRC was not removed from the sample, however using anchoring vignettes to adjust scores resulted in systematically lower observed scores after adjustment. Implications for measuring effort along with general conclusions about using invariance testing to evaluate anchoring vignettes is also provided