Entanglement frustration in multimode Gaussian states

Bipartite entanglement between two parties of a composite quantum system can be quantified in terms of the purity of one party and there always exists a pure state of the total system that maximizes it (and minimizes purity). When many different bipartitions are considered, the requirement that purity be minimal for all bipartitions gives rise to the phenomenon of entanglement frustration. This feature, observed in quantum systems with both discrete and continuous variables, can be studied by means of a suitable cost function whose minimizers are the maximally multipartite-entangled states (MMES). In this paper we extend the analysis of multipartite entanglement frustration of Gaussian states in multimode bosonic systems. We derive bounds on the frustration, under the constraint of finite mean energy, in the low and high energy limit.Comment: 4 pages, 2 figures. Contribution to "Folding and Unfolding: Interactions from Geometry. Workshop in honour of Giuseppe Marmo's 65th birthday", 8-12 June 2011, Ischia (NA) Ital

Invariant measures on multimode quantum Gaussian states

We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom -- the symplectic eigenvalues -- which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.Comment: 17 pages, comments are welcome. v2: presentation improved and typos corrected. Close to the published versio

Qubit-portraits of qudit states and quantum correlations

The machinery of qubit-portraits of qudit states, recently presented, is consider here in more details in order to characterize the presence of quantum correlations in bipartite qudit states. In the tomographic representation of quantum mechanics, Bell-like inequalities are interpreted as peculiar properties of a family of classical joint probability distributions which describe the quantum state of two qudits. By means of the qubit-portraits machinery a semigroup of stochastic matrices can be associated to a given quantum state. The violation of the CHSH inequalities is discussed in this framework with some examples, we found that quantum correlations in qutrit isotropic states can be detected by the suggested method while it cannot in the case of qutrit Werner states.Comment: 12 pages, 4 figure

On the classical capacity of quantum Gaussian channels

The set of quantum Gaussian channels acting on one bosonic mode can be classified according to the action of the group of Gaussian unitaries. We look for bounds on the classical capacity for channels belonging to such a classification. Lower bounds can be efficiently calculated by restricting to Gaussian encodings, for which we provide analytical expressions.Comment: 10 pages, IOP style. v2: minor corrections, close to the published versio

Synoptic/planetary-scale interactions and blocking over the North Atlantic Ocean

One segment of work in the past year focused on the diagnosis of a major blocking anticyclone and its interacting synoptic scale circulations that occurred during January 1979 over the North Atlantic Ocean. Another segment focused on the diagnosis of a second explosive cyclone development that occurred over the southeastern United States during the time of block formation. The diagnoses were accomplished using the diagnostic relationship known as the Zwack-Okossi (Z-O) development equation. Results indicate that in both cyclone cases the development occurred as a result of the favorable influence of positive vorticity advection, warm air advection, and latent heat release and ceased when one or more of these influences diminished. The advantages of the Z-O equation are described

Memory effects in attenuation and amplification quantum processes

With increasing communication rates via quantum channels, memory effects become unavoidable whenever the use rate of the channel is comparable to the typical relaxation time of the channel environment. We introduce a model of a bosonic memory channel, describing correlated noise effects in quantum-optical processes via attenuating or amplifying media. To study such a channel model, we make use of a proper set of collective field variables, which allows us to unravel the memory effects, mapping the n-fold concatenation of the memory channel to a unitarily equivalent, direct product of n single-mode bosonic channels. We hence estimate the channel capacities by relying on known results for the memoryless setting. Our findings show that the model is characterized by two different regimes, in which the cross correlations induced by the noise among different channel uses are either exponentially enhanced or exponentially reduced.Comment: 10 pages, 7 figures, close to the published versio

Dorsoventral patterning of the Xenopus eye involves differential temporal changes in the response of optic stalk and retinal progenitors to Hh signalling

Background: Hedgehog (Hh) signals are instrumental to the dorsoventral patterning of the vertebrate eye, promoting optic stalk and ventral retinal fates and repressing dorsal retinal identity. There has been limited analysis, however, of the critical window during which Hh molecules control eye polarity and of the temporal changes in the responsiveness of eye cells to these signals. Results: In this study, we used pharmacological and molecular tools to perform stage-specific manipulations of Hh signalling in the developing Xenopus eye. In gain-of-function experiments, most of the eye was sensitive to ventralization when the Hh pathway was activated starting from gastrula/neurula stages. During optic vesicle stages, the dorsal eye became resistant to Hh-dependent ventralization, but this pathway could partially upregulate optic stalk markers within the retina. In loss-of-function assays, inhibition of Hh signalling starting from neurula stages caused expansion of the dorsal retina at the expense of the ventral retina and the optic stalk, while the effects of Hh inhibition during optic vesicle stages were limited to the reduction of optic stalk size. Conclusions: Our results suggest the existence of two competence windows during which the Hh pathway differentially controls patterning of the eye region. In the first window, between the neural plate and the optic vesicle stages, Hh signalling exerts a global influence on eye dorsoventral polarity, contributing to the specification of optic stalk, ventral retina and dorsal retinal domains. In the second window, between optic vesicle and optic cup stages, this pathway plays a more limited role in the maintenance of the optic stalk domain. We speculate that this temporal regulation is important to coordinate dorsoventral patterning with morphogenesis and differentiation processes during eye development

A Multi-Objective Approach to Optimize a Periodic Maintenance Policy

The present paper proposes a multi-objective approach to find out an optimal periodic maintenance policy for a repairable and stochastically deteriorating multi-component system over a finite time horizon. The tackled problem concerns the determination of the system elements to replace at each scheduled and periodical system inspection by ensuring the simultaneous minimization of both the expected total maintenance cost and the expected global system unavailability time. It is assumed that in the case of system elements failure they are instantaneously detected and repaired by means of minimal repair actions in order to rapidly restore the system. A non-linear integer mathematical programming model is developed to solve the treated multi-objective problem whereas the Pareto optimal frontier is described by the Lexicographic Goal Programming and the \u3b5-constraint methods. To explain the whole procedure a case study is solved and the related considerations are given

A note on the realignment criterion

For a quantum state in a bipartite system represented as a density matrix, researchers used the realignment matrix and functions on its singular values to study the separability of the quantum state. We obtain bounds for elementary symmetric functions of singular values of realignment matrices. This answers some open problems proposed by Lupo, Aniello, and Scardicchio. As a consequence, we show that the proposed scheme by these authors for testing separability would not work if the two subsystems of the bipartite system have the same dimension.Comment: 11 pages, to appear in Journal of Physics A: Mathematical and Theoretica

Quantum reading under a local energy constraint

Nonclassical states of light play a central role in many quantum information protocols. Their quantum features have been exploited to improve the readout of information from digital memories, modelled as arrays of microscopic beam splitters [S. Pirandola, Phys. Rev. Lett. 106, 090504 (2011)]. In this model of quantum reading, a nonclassical source of light with Einstein-Podolski-Rosen correlations has been proven to retrieve more information than any classical source. In particular, the quantum-classical comparison has been performed under a global energy constraint, i.e., by fixing the mean total number of photons irradiated over each memory cell. In this paper we provide an alternative analysis which is based on a local energy constraint, meaning that we fix the mean number of photons per signal mode irradiated over the memory cell. Under this assumption, we investigate the critical number of signal modes after which a nonclassical source of light is able to beat any classical source irradiating the same number of signals.Comment: REVTeX. Published versio