The coloured quantum plane

We study the quantum plane associated to the coloured quantum group GL_{q}^{\lambda,\mu}(2) and solve the problem of constructing the corresponding differential geometric structure. This is achieved within the R-matrix framework generalising the Wess-Zumino formalism and leads to the concept of coloured quantum space. Both, the coloured Manin plane as well as the bicovariant differential calculus exhibit the colour exchange symmetry. The coloured h-plane corresponding to the coloured Jordanian quantum group GL_{h}^{\lambda,\mu}(2) is also obtained by contraction of the coloured q-plane.Comment: 10 pages, (AMS)LaTeX, to appear in J. Geom. Phy

Realisations of Quantum GL_p,q(2) and Jordanian GL_h,h'(2)

The quantum group GL_p,q(2) is known to be related to the Jordanian GL_h,h'(2) via a contraction procedure. It can also be realised using the generators of the Hopf algebra G_r,s. We contract the G_r,s quantum group to obtain its Jordanian analogue G_m,k, which provides a realisation of GL_h,h'(2) in a manner similar to the q-deformed case.Comment: 6 pages LaTex, Contribution to Proceedings of "8th International Colloquium on Quantum Groups and Integrable Systems", Prague, June 17 - 19, 199

Maximally discordant separable two qubit XX states

In a recent article S. Gharibian [\href{http://dx.doi.org/10.1103/PhysRevA.86.042106}{Phys. Rev. A {\bf 86}, 042106 (2012)}] has conjectured that no two qubit separable state of rank greater than two could be maximally non classical (defined to be those which have normalized geometric discord $1/4$) and asked for an analytic proof. In this work we prove analytically that among the subclass of $X$ states, there is a unique (up to local unitary equivalence) maximal separable state of rank two. Partial progress has been made towards the general problem and some necessary conditions have been derived.Comment: Preliminary draft, comment(s)/suggestion(s) welcome

Comment on "Sudden change in quantum discord accompanying the transition from bound to free entanglement"

In a recent article [http://dx.doi.org/10.1103/PhysRevA.87.022340, Phys. Rev. A 87, 022340 (2013)], Yan et al have studied geometric discord for a well known class of bound entangled states. Based on their calculation, they claim "It is found that there exists a nondynamic sudden change in quantum discord" for these states. In this Comment, we criticize their work by pointing out that what has been calculated is actually a bound, and not the exact value of discord. Since, generally, it is not possible to infer the exact value (or property) of a quantity just from its bound, we can not conclude about (exact) discord and its change. Thus, the above-mentioned conclusion can not be drawn from the calculations of the paper.Comment: 1 pag

Architecting the cyberinfrastructure for National Science Foundation Ocean Observatories Initiative (OOI)

The NSF Ocean Observatories Initiative (OOI) is a networked ocean research observatory with arrays of instrumented water column moorings and buoys, profilers, gliders and autonomous underwater vehicles (AUV) within different open ocean and coastal regions. OOI infrastructure also includes a cabled array of instrumented seafloor platforms and water column moorings on the Juan de Fuca tectonic plate. This networked system of instruments, moored and mobile platforms, and arrays will provide ocean scientists, educators and the public the means to collect sustained, time-series data sets that will enable examination of complex, interlinked physical, chemical, biological, and geological processes operating throughout the coastal regions and open ocean. The seven arrays built and deployed during construction support the core set of OOI multidisciplinary scientific instruments that are integrated into a networked software system that will process, distribute, and store all acquired data. The OOI has been built with an expectation of operation for 25 years.Peer Reviewe