The axial ratio of hcp iron at the conditions of the Earth's inner core

We present ab initio calculations of the high-temperature axial c/a ratio of hexagonal-close-packed (hcp) iron at Earth's core pressures, in order to help interpret the observed seismic anisotropy of the inner core. The calculations are based on density functional theory, which is known to predict the properties of high-pressure iron with good accuracy. The temperature dependence of c/a is determined by minimising the Helmholtz free energy at fixed volume and temperature, with thermal contributions due to lattice vibrations calculated using harmonic theory. Anharmonic corrections to the harmonic predictions are estimated from calculations of the thermal average stress obtained from ab initio molecular dynamics simulations of hcp iron at the conditions of the inner core. We find a very gradual increase of axial ratio with temperature. This increase is much smaller than found in earlier calculations, but is in reasonable agreement with recent high-pressure, high-temperature diffraction measurements. This result casts doubt on an earlier interpretation of the seismic anisotropy of the inner core

Demonstration of entanglement-by-measurement of solid state qubits

Projective measurements are a powerful tool for manipulating quantum states. In particular, a set of qubits can be entangled by measurement of a joint property such as qubit parity. These joint measurements do not require a direct interaction between qubits and therefore provide a unique resource for quantum information processing with well-isolated qubits. Numerous schemes for entanglement-by-measurement of solid-state qubits have been proposed, but the demanding experimental requirements have so far hindered implementations. Here we realize a two-qubit parity measurement on nuclear spins in diamond by exploiting the electron spin of a nitrogen-vacancy center as readout ancilla. The measurement enables us to project the initially uncorrelated nuclear spins into maximally entangled states. By combining this entanglement with high-fidelity single-shot readout we demonstrate the first violation of Bells inequality with solid-state spins. These results open the door to a new class of experiments in which projective measurements are used to create, protect and manipulate entanglement between solid-state qubits.Comment: 6 pages, 4 figure

Dissecting the genetic basis for seed coat mucilage heteroxylan biosynthesis in plantago ovata using gamma irradiation and infrared spectroscopy

Seeds from the myxospermous species Plantago ovata release a polysaccharide-rich mucilage upon contact with water. This seed coat derived mucilage is composed predominantly of heteroxylan (HX) and is utilized as a gluten-free dietary fiber supplement to promote human colorectal health. In this study, a gamma-irradiated P. ovata population was generated and screened using histological stains and Fourier Transform Mid Infrared (FTMIR) spectroscopy to identify putative mutants showing defects in seed coat mucilage HX composition and/or structure. FTMIR analysis of dry seed revealed variation in regions of the IR spectra previously linked to xylan structure in Secale cereale (rye). Subsequent absorbance ratio and PCA multivariate analysis identified 22 putative mutant families with differences in the HX IR fingerprint region. Many of these showed distinct changes in the amount and subtle changes in structure of HX after mucilage extrusion, while 20% of the putative HX mutants identified by FTMIR showed no difference in staining patterns of extruded mucilage compared to wild-type. Transcriptional screening analysis of two putative reduced xylan in mucilage (rxm) mutants, rxm1 and rxm3, revealed that changes in HX levels in rxm1 correlate with reduced transcription of known and novel genes associated with xylan synthesis, possibly indicative of specific co-regulatory units within the xylan biosynthetic pathway. These results confirm that FTMIR is a suitable method for identifying putative mutants with altered mucilage HX composition in P. ovata, and therefore forms a resource to identify novel genes involved in xylan biosynthesis.Matthew R. Tucker, Chao Ma, Jana Phan, Kylie Neumann, Neil J. Shirley, Michael G. Hahn, Daniel Cozzolino and Rachel A. Burto

The Significance of the CC-Numerical Range and the Local CC-Numerical Range in Quantum Control and Quantum Information

This paper shows how C-numerical-range related new strucures may arise from practical problems in quantum control--and vice versa, how an understanding of these structures helps to tackle hot topics in quantum information. We start out with an overview on the role of C-numerical ranges in current research problems in quantum theory: the quantum mechanical task of maximising the projection of a point on the unitary orbit of an initial state onto a target state C relates to the C-numerical radius of A via maximising the trace function |\tr \{C^\dagger UAU^\dagger\}|. In quantum control of n qubits one may be interested (i) in having U\in SU(2^n) for the entire dynamics, or (ii) in restricting the dynamics to {\em local} operations on each qubit, i.e. to the n-fold tensor product SU(2)\otimes SU(2)\otimes >...\otimes SU(2). Interestingly, the latter then leads to a novel entity, the {\em local} C-numerical range W_{\rm loc}(C,A), whose intricate geometry is neither star-shaped nor simply connected in contrast to the conventional C-numerical range. This is shown in the accompanying paper (math-ph/0702005). We present novel applications of the C-numerical range in quantum control assisted by gradient flows on the local unitary group: (1) they serve as powerful tools for deciding whether a quantum interaction can be inverted in time (in a sense generalising Hahn's famous spin echo); (2) they allow for optimising witnesses of quantum entanglement. We conclude by relating the relative C-numerical range to problems of constrained quantum optimisation, for which we also give Lagrange-type gradient flow algorithms.Comment: update relating to math-ph/070200

On the Equivalence Between Type I Liouville Dynamical Systems in the Plane and the Sphere

Producción CientíficaSeparable Hamiltonian systems either in sphero-conical coordinates on an S2 sphere or in elliptic coordinates on a R2 plane are described in a unified way. A back and forth route connecting these Liouville Type I separable systems is unveiled. It is shown how the gnomonic projection and its inverse map allow us to pass from a Liouville Type I separable system with a spherical configuration space to its Liouville Type I partners where the configuration space is a plane and back. Several selected spherical separable systems and their planar cousins are discussed in a classical context

Quark deconfinement in neutron star cores and the ground state of neutral matter

Whether or not deconfined quark phase exists in neutron star cores and represents the ground state of neutral matter at moderate densities are open questions. We use two realistic effective quark models, the three-flavor Nambu-Jona-Lasinio model and the modified quark-meson coupling model, to describe the neutron star matter. After constructing possible hybrid equations of state (EOSes) with unpaired or color superconducting quark phase, we systematically discuss the observational constraints of neutron stars on the EOSes. It is found that the neutron star with pure quark matter core is unstable and the hadronic phase with hyperons is denied, while hybrid EOSes with two-flavor color superconducting phase or unpaired quark matter phase are both allowed by the tight and most reliable constraints from two stars Ter 5 I and EXO 0748-676. And the hybrid EOS with unpaired quark matter phase is allowed even compared with the tightest constraint from the most massive pulsar star PSR J0751+1807. Therefore, we conclude that the ground state of neutral matter at moderate densities is in deconfined quark phase likely.Comment: 13 pages, 4 figure

Stochastic Renormalization Group in Percolation: I. Fluctuations and Crossover

A generalization of the Renormalization Group, which describes order-parameter fluctuations in finite systems, is developed in the specific context of percolation. This ``Stochastic Renormalization Group'' (SRG) expresses statistical self-similarity through a non-stationary branching process. The SRG provides a theoretical basis for analytical or numerical approximations, both at and away from criticality, whenever the correlation length is much larger than the lattice spacing (regardless of the system size). For example, the SRG predicts order-parameter distributions and finite-size scaling functions for the complete crossover between phases. For percolation, the simplest SRG describes structural quantities conditional on spanning, such as the total cluster mass or the minimum chemical distance between two boundaries. In these cases, the Central Limit Theorem (for independent random variables) holds at the stable, off-critical fixed points, while a ``Fractal Central Limit Theorem'' (describing long-range correlations) holds at the unstable, critical fixed point. This first part of a series of articles explains these basic concepts and a general theory of crossover. Subsequent parts will focus on limit theorems and comparisons of small-cell SRG approximations with simulation results.Comment: 33 pages, 6 figures, to appear in Physica A; v2: some typos corrected and Eqs. (26)-(27) cast in a simpler (but equivalent) for

Preparation and Measurement of Three-Qubit Entanglement in a Superconducting Circuit

Traditionally, quantum entanglement has played a central role in foundational discussions of quantum mechanics. The measurement of correlations between entangled particles can exhibit results at odds with classical behavior. These discrepancies increase exponentially with the number of entangled particles. When entanglement is extended from just two quantum bits (qubits) to three, the incompatibilities between classical and quantum correlation properties can change from a violation of inequalities involving statistical averages to sign differences in deterministic observations. With the ample confirmation of quantum mechanical predictions by experiments, entanglement has evolved from a philosophical conundrum to a key resource for quantum-based technologies, like quantum cryptography and computation. In particular, maximal entanglement of more than two qubits is crucial to the implementation of quantum error correction protocols. While entanglement of up to 3, 5, and 8 qubits has been demonstrated among spins, photons, and ions, respectively, entanglement in engineered solid-state systems has been limited to two qubits. Here, we demonstrate three-qubit entanglement in a superconducting circuit, creating Greenberger-Horne-Zeilinger (GHZ) states with fidelity of 88%, measured with quantum state tomography. Several entanglement witnesses show violation of bi-separable bounds by 830\pm80%. Our entangling sequence realizes the first step of basic quantum error correction, namely the encoding of a logical qubit into a manifold of GHZ-like states using a repetition code. The integration of encoding, decoding and error-correcting steps in a feedback loop will be the next milestone for quantum computing with integrated circuits.Comment: 7 pages, 4 figures, and Supplementary Information (4 figures)

An introduction to Graph Data Management

A graph database is a database where the data structures for the schema and/or instances are modeled as a (labeled)(directed) graph or generalizations of it, and where querying is expressed by graph-oriented operations and type constructors. In this article we present the basic notions of graph databases, give an historical overview of its main development, and study the main current systems that implement them

Topologically Protected Quantum State Transfer in a Chiral Spin Liquid

Topology plays a central role in ensuring the robustness of a wide variety of physical phenomena. Notable examples range from the robust current carrying edge states associated with the quantum Hall and the quantum spin Hall effects to proposals involving topologically protected quantum memory and quantum logic operations. Here, we propose and analyze a topologically protected channel for the transfer of quantum states between remote quantum nodes. In our approach, state transfer is mediated by the edge mode of a chiral spin liquid. We demonstrate that the proposed method is intrinsically robust to realistic imperfections associated with disorder and decoherence. Possible experimental implementations and applications to the detection and characterization of spin liquid phases are discussed.Comment: 14 pages, 7 figure