We have used low-field ¹H nuclear-magnetic resonance (NMR) spectroscopy and molecular dynamics (MD) to investigate the aggregation dynamics of magnetic particles in ionic ferrofluids (IFFs) in the presence of magnetic field gradients. At the beginning of the experiments, the measured NMR spectra were broad and asymmetric, exhibiting two features attributed to different dynamical environments of water protons, depending on the local strength of the field gradients. Hence, the spatial redistribution of the magnetic particles in the ferrofluid caused by the presence of an external magnetic field in a time scale of minutes can be monitored in real time, following the changes in the features of the NMR spectra during a period of about an hour. As previously reported [Heinrich et al., Phys. Rev. Lett., 2011, 106, 208301], in the homogeneous magnetic field of a NMR spectrometer, the aggregation of the particles of the IFF proceeds in two stages. The first stage corresponds to the gradual aggregation of monomers prior to and during the formation of chain-like structures. The second stage proceeds after the chains have reached a critical average length, favoring lateral association of the strings into hexagonal zipped-chain superstructures or bundles. In this work, we focus on the influence of a strongly inhomogeneous magnetic field on the aforementioned aggregation dynamics. The main observation is that, as the sample is immersed in a certain magnetic field gradient and kept there for a time τ_inh, magnetophoresis rapidly converts the ferrofluid into an aggregation state which finds its correspondence to a state on the evolution curve of the pristine sample in a homogeneous field. From the degree of aggregation reached at the time τ_inh, the IFF sample just evolves thereafter in the homogeneous field of the NMR spectrometer in exactly the same way as the pristine sample. The final equilibrium state always consists of a colloidal suspension of zipped-chain bundles with the chain axes aligned along the magnetic field direction.

A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a projector associated with an observable, and interpret it as the probability of obtaining the outcome corresponding to that projector. We make use of fidelity-based metrics such as angle, Bures, and root infidelity to propose a measure of uncertainty. The triangle inequality allows us to derive a family of uncertainty relations. In the case of the angle metric, we recover the Landau-Pollak inequality for pure states and show, in a natural way, how to extend it to the case of mixed states in arbitrary dimension. In addition, we derive and compare alternative uncertainty relations when using other known fidelity-based metrics. DOI: http://dx.doi.org/10.1103/PhysRevA.89.034101 ©2014 American Physical Society

In this work we study the properties of a purification-based entropic metric for measuring the distance between both quantum states and quantum processes. This metric is defined as the square root of the entropy of the average of two purifications of mixed quantum states which maximize the overlap between the purified states. We analyze this metric and show that it satisfies many appealing properties, which suggest this metric is an interesting proposal for theoretical and experimental applications of quantum information. DOI: http://dx.doi.org/10.1103/PhysRevA.87.062319 ©2013 American Physical Society

We introduce a new family of quantum distances based on symmetric Csiszár divergences, a class of distinguishability measures that encompass the main dissimilarity measures between probability distributions. We prove that these quantum distances can be obtained by optimizing over a set of quantum measurements followed by a purification process. Specifically, we address in the first place the case of distinguishing pure quantum states, solving an optimization of the symmetric Csiszár divergences over von Neumann measurements. In the second place, by making use of the concept of purification of quantum states, we arrive at a new set of distinguishability measures, which we call extended quantum Csiszár distances. In addition, as it has been demonstrated that a purification process can be physically implemented, the proposed distinguishability measures for quantum states could be endowed with an operational interpretation. Finally, by taking advantage of a well-known result for classical Csiszár divergences, we show how to build quantum Csiszár true distances. Thus, our main contribution is the development and analysis of a method for obtaining quantum distances satisfying the triangle inequality in the space of quantum states for Hilbert spaces of arbitrary dimension.