Tristán M. Osán

Monoparametric family of metrics derived from classical Jensen–Shannon divergence

Abstract Jensen–Shannon divergence is a well known multi-purpose measure of dissimilarity between probability distributions. It has been proven that the square root of this quantity is a true metric in the sense that, in addition to the basic properties of a distance, it also satisfies the triangle inequality. In this work we extend this last result to prove that in fact it is possible to derive a monoparametric family of metrics from the classical Jensen–Shannon divergence. Motivated by our results, an application into the field of symbolic sequences segmentation is explored. Additionally, we analyze the possibility to extend this result into the quantum realm.

Purification-based metric to measure the distance between quantum states and processes

Fil: Osan, Tristan Martin. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - Cordoba. Instituto de Fisica Enrique Gaviola. Universidad Nacional de Cordoba. Instituto de Fisica Enrique Gaviola; Argentina

Problem of quantifying quantum correlations with non-commutative discord

In this work we analyze a non-commutativity measure of quantum correlations recently proposed by Guo (Sci Rep 6:25241, 2016). By resorting to a systematic survey of a two-qubit system, we detected an undesirable behavior of such a measure related to its representation-dependence. In the case of pure states, this dependence manifests as a non-satisfactory entanglement measure whenever a representation other than the Schmidt’s is used. In order to avoid this basis-dependence feature, we argue that a minimization procedure over the set of all possible representations of the quantum state is required. In the case of pure states, this minimization can be analytically performed and the optimal basis turns out to be that of Schmidt’s. In addition, the resulting measure inherits the main properties of Guo’s measure and, unlike the latter, it reduces to a legitimate entanglement measure in the case of pure states. Some examples involving general mixed states are also analyzed considering such an optimization. The results show that, in most cases of interest, the use of Guo’s measure can result in an overestimation of quantum correlations. However, since Guo’s measure has the advantage of being easily computable, it might be used as a qualitative estimator of the presence of quantum correlations.

Beyond Landau–Pollak and entropic inequalities: Geometric bounds imposed on uncertainties sums

In this paper we propose generalized inequalities to quantify the uncertainty principle. We deal with two observables with finite discrete spectra described by positive operator-valued measures (POVM) and with systems in mixed states. Denoting by p(A;ρ) and p(B;ρ) the probability vectors associated with observables A and B when the system is in the state ρ, we focus on relations of the form Uα(p(A;ρ))+Uβ(p(B;ρ))≥Bα,β(A,B) where Uλ is a measure of uncertainty and B is a non-trivial state-independent bound for the uncertainty sum. We propose here: (i) an extension of the usual Landau–Pollak inequality for uncertainty measures of the form Uf(p(A;ρ)) = f(maxipi(A;ρ)) issued from well suited metrics; our generalization comes out as a consequence of the triangle inequality. The original Landau–Pollak inequality initially proved for nondegenerate observables and pure states, appears to be the most restrictive one in terms of the maximal probabilities; (ii) an entropic formulation for which the uncertainty measur...

A study of the bis(4-chlorophenyl) sulphide by 35Cl nuclear quadrupole resonance and ab initio calculations

As an extension of previous works in sulphur-substituted biphenyls, a complete pulsed 35Cl nuclear quadrupole resonance (NQR) study of the bis(4-chlorophenyl) sulphide compound is presented. In order to characterize the structural thermal behaviour of the solid phase, the NQR spectra and spin-lattice relaxation times were recorded from 80 K to 330 K. In addition, ab initio calculations at HF/3-21G* and 6-31G* levels were performed in order to obtain information about the equilibrium geometry and the torsional potential of the free bis(4-chlorophenyl) sulphide molecule. The NQR study results show that the title compound presents a unique stable crystalline phase in the scanned temperature range. This phase diagram contrasts notably with those observed at the same temperatures in bis(4-chlorophenyl) sulphone and bis(4-chlorophenyl) sulphoxide, which show an incommensurate phase transition and two-phase coexistence, respectively. The narrow NQR line observed suggests that the 35Cl atoms in the unit cell are in crystallographic equivalent positions. Ab initio calculations for the free molecule show that the symmetry point group is C2 and the dihedral angle is 60°. The results are discussed and compared with the known information about the sulphone and sulphoxide derivatives. The effect of the interphenyl linking group is also discussed, in order to understand the evolution of the phase diagram in this group of compounds.

NQR study of bis(4-chlorophenyl)sulphoxide

A pulsed nuclear quadrupolar resonance (NQR) study was performed on bis(4-chlorophenyl)sulphoxide. In order to characterize the structural thermal behaviour, the NQR spectra were recorded from 80 to 350 K. The results suggest the coexistence of two crystalline phases over the whole scanned temperature range. In spite of the very close molecular structure of the compound with the bis(4-chlorophenyl)sulphone, there is no evidence of any incommensurate phase transition. This fact demonstrates the fundamental role of the molecular group linking phenyl rings in the appearance of a normal - incommensurate phase transition in biphenyl-type compounds.