On the quantumness of correlations in nuclear magnetic resonance

Nuclear Magnetic Resonance (NMR) was successfully employed to test several protocols and ideas in Quantum Information Science. In most of these implementations the existence of entanglement was ruled out. This fact introduced concerns and questions about the quantum nature of such bench tests. In this article we address some issues related to the non-classical aspects of NMR systems. We discuss some experiments where the quantum aspects of this system are supported by quantum correlations of separable states. Such quantumness, beyond the entanglement-separability paradigm, is revealed via a departure between the quantum and the classical versions of information theory. In this scenario, the concept of quantum discord seems to play an important role. We also present an experimental implementation of an analogous of the single-photon Mach-Zehnder interferometer employing two nuclear spins to encode the interferometric paths. This experiment illustrate how non-classical correlations of separable states may be used to simulate quantum dynamics. The results obtained are completely equivalent to the optical scenario, where entanglement (between two field modes) may be present

Inverse Additive Problems for Minkowski Sumsets II

The Brunn-Minkowski Theorem asserts that $\mu_d(A+B)^{1/d}\geq \mu_d(A)^{1/d}+\mu_d(B)^{1/d}$ for convex bodies $A,\,B\subseteq \R^d$, where $\mu_d$ denotes the $d$-dimensional Lebesgue measure. It is well-known that equality holds if and only if $A$ and $B$ are homothetic, but few characterizations of equality in other related bounds are known. Let $H$ be a hyperplane. Bonnesen later strengthened this bound by showing $$\mu_d(A+B)\geq (M^{1/(d-1)}+N^{1/(d-1)})^{d-1}(\frac{\mu_d(A)}{M}+\frac{\mu_d(B)}{N}),$$ where $M=\sup\{\mu_{d-1}((\mathbf x+H)\cap A)\mid \mathbf x\in \R^d\}$ and $N=\sup\{\mu_{d-1}((\mathbf y+H)\cap B)\mid \mathbf y\in \R^d\}$. Standard compression arguments show that the above bound also holds when $M=\mu_{d-1}(\pi(A))$ and $N=\mu_{d-1}(\pi(B))$, where $\pi$ denotes a projection of $\mathbb R^d$ onto $H$, which gives an alternative generalization of the Brunn-Minkowski bound. In this paper, we characterize the cases of equality in this later bound, showing that equality holds if and only if $A$ and $B$ are obtained from a pair of homothetic convex bodies by `stretching' along the direction of the projection, which is made formal in the paper. When $d=2$, we characterize the case of equality in the former bound as well

Orbital current mode in elliptical quantum dots

An orbital current mode peculiar to deformed quantum dots is theoretically investigated; first by using a simple model that allows to interpret analytically its main characteristics, and second, by numerically solving the microscopic equations of time evolution after an initial perturbation within the time-dependent local-spin-density approximation. Results for different deformations and sizes are shown.Comment: 4 REVTEX pages, 4 PDF figures, accepted in PRB:R

Nonclassical correlation in NMR quadrupolar systems

The existence of quantum correlation (as revealed by quantum discord), other than entanglement and its role in quantum-information processing (QIP), is a current subject for discussion. In particular, it has been suggested that this nonclassical correlation may provide computational speedup for some quantum algorithms. In this regard, bulk nuclear magnetic resonance (NMR) has been successfully used as a test bench for many QIP implementations, although it has also been continuously criticized for not presenting entanglement in most of the systems used so far. In this paper, we report a theoretical and experimental study on the dynamics of quantum and classical correlations in an NMR quadrupolar system. We present a method for computing the correlations from experimental NMR deviation-density matrices and show that, given the action of the nuclear-spin environment, the relaxation produces a monotonic time decay in the correlations. Although the experimental realizations were performed in a specific quadrupolar system, the main results presented here can be applied to whichever system uses a deviation-density matrix formalism.Comment: Published versio

Scattering of Woods-Saxon Potential in Schrodinger Equation

The scattering solutions of the one-dimensional Schrodinger equation for the Woods-Saxon potential are obtained within the position-dependent mass formalism. The wave functions, transmission and reflection coefficients are calculated in terms of Heun's function. These results are also studied for the constant mass case in detail.Comment: 14 page

Far-infrared edge modes in quantum dots

We have investigated edge modes of different multipolarity sustained by quantum dots submitted to external magnetic fields. We present a microscopic description based on a variational solution of the equation of motion for any axially symmetric confining potential and multipole mode. Numerical results for dots with different number of electrons whose ground-state is described within a local Current Density Functional Theory are discussed. Two sum rules, which are exact within this theory, are derived. In the limit of a large neutral dot at B=0, we have shown that the classical hydrodynamic dispersion law for edge waves \omega(q) \sim \sqrt{q \ln (q_0/q)} holds when quantum and finite size effects are taken into account.Comment: We have changed some figures as well as a part of the tex

Far-infrared edge modes in quantum dots

We have investigated edge modes of different multipolarity sustained by quantum dots submitted to external magnetic fields. We present a microscopic description based on a variational solution of the equation of motion for any axially symmetric confining potential and multipole mode. Numerical results for dots with different number of electrons whose ground-state is described within a local Current Density Functional Theory are discussed. Two sum rules, which are exact within this theory, are derived. In the limit of a large neutral dot at B=0, we have shown that the classical hydrodynamic dispersion law for edge waves \omega(q) \sim \sqrt{q \ln (q_0/q)} holds when quantum and finite size effects are taken into account.Comment: We have changed some figures as well as a part of the tex