Observable measure of quantum coherence in finite dimensional systems

Quantum coherence is the key resource for quantum technology, with applications in quantum optics, information processing, metrology, and cryptography. Yet, there is no universally efficient method for quantifying coherence either in theoretical or in experimental practice. I introduce a framework for measuring quantum coherence in finite dimensional systems. I define a theoretical measure which satisfies the reliability criteria established in the context of quantum resource theories. Then, I present an experimental scheme implementable with current technology which evaluates the quantum coherence of an unknown state of a d-dimensional system by performing two programmable measurements on an ancillary qubit, in place of the O(d2) direct measurements required by full state reconstruction. The result yields a benchmark for monitoring quantum effects in complex systems, e.g., certifying nonclassicality in quantum protocols and probing the quantum behavior of biological complexes

Quantum discord for general two-qubit states: Analytical progress

We present a reliable algorithm to evaluate quantum discord for general two-qubit states, amending and extending an approach recently put forward for the subclass of X states. A closed expression for the discord of arbitrary states of two qubits cannot be obtained, as the optimization problem for the conditional entropy requires the solution to a pair of transcendental equations in the state parameters. We apply our algorithm to run a numerical comparison between quantum discord and an alternative, computable measure of nonclassical correlations, namely, the geometric discord. We identify the extremally nonclassically correlated two-qubit states according to the (normalized) geometric discord, at a fixed value of the conventional quantum discord. The latter cannot exceed the square root of the former for systems of two qubits. © 2011 American Physical Society

Interplay between computable measures of entanglement and other quantum correlations

Composite quantum systems can be in generic states characterized not only by entanglement but also by more general quantum correlations. The interplay between these two signatures of nonclassicality is still not completely understood. In this work we investigate this issue, focusing on computable and observable measures of such correlations: entanglement is quantified by the negativity N, while general quantum correlations are measured by the (normalized) geometric quantum discord DG. For two-qubit systems, we find that the geometric discord reduces to the squared negativity on pure states, while the relationship DGN2 holds for arbitrary mixed states. The latter result is rigorously extended to pure, Werner, and isotropic states of two-qudit systems for arbitrary d, and numerical evidence of its validity for arbitrary states of a qubit and a qutrit is provided as well. Our results establish an interesting hierarchy, which we conjecture to be universal, between two relevant and experimentally friendly nonclassicality indicators. This ties in with the intuition that general quantum correlations should at least contain and in general exceed entanglement on mixed states of composite quantum systems. © 2011 American Physical Society

Effect of electrical stimulation and others genetic and environmental factors on colour of lamb meat

The research aimed to assess the effect of breed, sex, age at slaughter, rearing system and electrical stimulation on some colorimetric characteristics measured on the muscles Longissimus dorsi (LD), Gluteobiceps (Gb), Semimembranosus (Sm) and Rectus femoris (RF) of lambs belonging to the genetic types Gentile di Puglia (GP), Ile de France (IF) and the cross-breeds F1, F2 and F3. The IF lambs provided meat with the highest value of hue and lightness and the lowest chroma and redness. The F1 lambs showed the highest values of redness while the F2 crossbreed significantly differed from the other three genetic types only in pH, which was always the lowest. The F3 crossbreed revealed similar behaviour to the other genetic types, except for the pH which was always higher than in GP, F1 and F2. The differences between sexes were restricted to L* and pH values, being higher in the male. The lambs slaughtered at 56 days showed high a* values, while b* and hue were on average higher in younger lambs (35 days). The lambs reared with maternal milk in comparison with the artificially reared ones provided meat with the highest a* chroma and b* and the lowest hue values. Electrical stimulation of the carcass seems to have produced the same effects as the usual ageing time in cold store. The RF muscle provided the brightest meat; Sm showed the highest values of b* and chroma; LD provided the “darkest” meat and the lowest values of b* and hue; Gb produced a lower a* value than muscles LD, RF and Sm

Observable measure of bipartite quantum correlations

We introduce a measure Q of bipartite quantum correlations for arbitrary two-qubit states, expressed as a state-independent function of the density matrix elements. The amount of quantum correlations can be quantified experimentally by measuring the expectation value of a small set of observables on up to four copies of the state, without the need for a full tomography. We extend the measure to 2×d systems, providing its explicit form in terms of observables and applying it to the relevant class of multiqubit states employed in the deterministic quantum computation with one quantum bit model. The number of required measurements to determine Q in our scheme does not increase with d. Our results provide an experimentally friendly framework to estimate quantitatively the degree of general quantum correlations in composite systems. © 2012 American Physical Society

Witnessing multipartite entanglement by detecting asymmetry

The characterization of quantum coherence in the context of quantum information theory and its interplay with quantum correlations is currently subject of intense study. Coherence in a Hamiltonian eigenbasis yields asymmetry, the ability of a quantum system to break a dynamical symmetry generated by the Hamiltonian. We here propose an experimental strategy to witness multipartite entanglement in many-body systems by evaluating the asymmetry with respect to an additive Hamiltonian. We test our scheme by simulating asymmetry and entanglement detection in a three-qubit Greenberger-Horne-Zeilinger (GHZ) diagonal state

Discussion of "Sequential Quasi-Monte Carlo" by Mathieu Gerber and Nicolas Chopin

A discussion on the possibility of reducing the variance of quasi-Monte Carlo estimators in applications. Further details are provided in the accompanying paper "Variance Reduction for Quasi-Monte Carlo"

Measuring gaussian quantum information and correlations using the Rényi entropy of order 2

We demonstrate that the Rényi-2 entropy provides a natural measure of information for any multimode Gaussian state of quantum harmonic systems, operationally linked to the phase-space Shannon sampling entropy of the Wigner distribution of the state. We prove that, in the Gaussian scenario, such an entropy satisfies the strong subadditivity inequality, a key requirement for quantum information theory. This allows us to define and analyze measures of Gaussian entanglement and more general quantum correlations based on such an entropy, which are shown to satisfy relevant properties such as monogamy. © 2012 American Physical Society

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

Dynamics of a slowly-varying sand bed in a circular pipe

The long wave-length dynamics and stability of a bed of sand occupying the lower segment of a circular pipe are studied analytically up to first-order in the small parameter characterizing the slope of the bed. The bed is assumed to be at rest, with at most a thin sand layer (the bedload) moving at the sheared interface. When the sand bed is plane, with depth independent of position z along the axis of the pipe, the velocity of the liquid is known from previous studies of stratified laminar flow of two Newtonian liquids (the lower one with infinite viscosity representing the sand bed). When the depth of the sand bed varies with z, secondary flows develop in the cross-sectional (x, y) plane, and these are computed numerically, assuming that the sand bed remains a straight horizontal line in the cross-sectional plane. The mean shear stress acting on the perturbed sand bed is then determined both from the computed secondary flows and by means of the averaged equations of Luchini and Charru. The latter approach requires knowledge only of the flow over the unperturbed, flat sand bed, combined with an accurate approximation of the distribution of the perturbed stresses between the pipe wall and the sand bed. The perturbed stresses determined by the two methods agree well with each other. Using these stresses, it is then possible to apply standard theories of bed stability to determine the balance between the destabilizing effect of inertial (out-of-phase) stresses and the stabilizing effects of gravity and relaxation of the particle flux, and various examples are considered