Overcoming a limitation of deterministic dense coding with a non-maximally entangled initial state

Under two-party deterministic dense-coding, Alice communicates (perfectly distinguishable) messages to Bob via a qudit from a pair of entangled qudits in pure state |Psi>. If |Psi> represents a maximally entangled state (i.e., each of its Schmidt coefficients is sqrt(1/d)), then Alice can convey to Bob one of d^2 distinct messages. If |Psi> is not maximally entangled, then Ji et al. [Phys. Rev. A 73, 034307 (2006)] have shown that under the original deterministic dense-coding protocol, in which messages are encoded by unitary operations performed on Alice's qudit, it is impossible to encode d^2-1 messages. Encoding d^2-2 is possible; see, e.g., the numerical studies by Mozes et al. [Phys. Rev. A 71, 012311 (2005)]. Answering a question raised by Wu et al. [Phys. Rev. A 73, 042311 (2006)], we show that when |Psi> is not maximally entangled, the communications limit of d^2-2 messages persists even when the requirement that Alice encode by unitary operations on her qudit is weakened to allow encoding by more general quantum operators. We then describe a dense-coding protocol that can overcome this limitation with high probability, assuming the largest Schmidt coefficient of |Psi> is sufficiently close to sqrt(1/d). In this protocol, d^2-2 of the messages are encoded via unitary operations on Alice's qudit, and the final (d^2-1)-th message is encoded via a (non-trace-preserving) quantum operation.Comment: 18 pages, published versio

Avian cerebellar floccular fossa size is not a proxy for flying ability in birds

Extinct animal behavior has often been inferred from qualitative assessments of relative brain region size in fossil endocranial casts. For instance, flight capability in pterosaurs and early birds has been inferred from the relative size of the cerebellar flocculus, which in life protrudes from the lateral surface of the cerebellum. A primary role of the flocculus is to integrate sensory information about head rotation and translation to stabilize visual gaze via the vestibulo-occular reflex (VOR). Because gaze stabilization is a critical aspect of flight, some authors have suggested that the flocculus is enlarged in flying species. Whether this can be further extended to a floccular expansion in highly maneuverable flying species or floccular reduction in flightless species is unknown. Here, we used micro computed-tomography to reconstruct “virtual” endocranial casts of 60 extant bird species, to extract the same level of anatomical information offered by fossils. Volumes of the floccular fossa and entire brain cavity were measured and these values correlated with four indices of flying behavior. Although a weak positive relationship was found between floccular fossa size and brachial index, no significant relationship was found between floccular fossa size and any other flight mode classification. These findings could be the result of the bony endocranium inaccurately reflecting the size of the neural flocculus, but might also reflect the importance of the flocculus for all modes of locomotion in birds. We therefore conclude that the relative size of the flocculus of endocranial casts is an unreliable predictor of locomotor behavior in extinct birds, and probably also pterosaurs and non-avian dinosaurs

Propylthiocyclopentadiene: A new synthetic route to complexes of iron and group 4 transition metals. Molecular structure of (C5H4SCH2CH2CH3)(2)ZrCl2

The use of the propylthio-substituted cyclopentadienylsodium salt leads to 1,1'-bis(propylthio) ferrocene and dichlorobis(propylthiocyclopentadienyl)zirconium, titanium or hafnium(IV). The structure of (C5H4SCH2CH2CH3)(2)ZrCl2 has been established by X-ray analysis (orthorhombic, Pbcn, a = 11.943(1) Angstrom, b = 6.883(2) Angstrom, c = 22.412(2) Angstrom, V = 1842.4(2) Angstrom(3), Z = 4, R(F) = 0.027). The complexes have been characterized by H-1 and C-13 NMR and electrochemical studies. The physico chemical properties of 1,1'-bis(propylthio) ferrocene are discussed by a molecular approach at the extended Huckel level

Melting of a Two-component Source beneath Iceland

New trace element and Hf-Nd isotope data on post-glacial basalts from Iceland's main rift zones are used in conjunction with literature data to evaluate the relative importance of source heterogeneity and the melting process for the final melt composition. Correlations between Hf and Nd isotope compositions and trace element ratios indicate that at least two source components are sampled systematically as a function of the degree and pressure of melting beneath Iceland. Strong depletion in Rb, Ba, U and Th and enrichment in Nb and Ta compared with La in the most enriched samples from the Reykjanes Peninsula and Western Rift Zone suggests that the enriched source component is similar to ancient recycled enriched mid-ocean ridge basalt (E-MORB) crust. Highly incompatible trace element ratios such as Nb/La and Nb/U and Pb isotope ratios are variable across Iceland. This observation suggests that either the enriched component is intrinsically heterogeneous, or that there is a larger proportion of the enriched source component beneath the Southwestern Rift Zone compared with the Northern Rift Zone. The relative effect of source heterogeneity and melting on the final melt composition was evaluated with a one-dimensional polybaric melt mixing model in which accumulated melts from a depleted MORB mantle and a recycled E-MORB crust are mixed in different ways. Two styles of melt mixing were simulated: (1) complete mixing of melts with variable proportions of the depleted mantle and recycled E-MORB components; (2) incomplete mixing with a fixed initial proportion of the two source components. Calculated pressure-dependent compositional changes using these simple two-component melting models can explain the observed trends in trace element ratio and isotope ratio diagrams for Icelandic basalts, even in cases where conventional binary mixing models would require more than two source components. The example of Iceland demonstrates that melt mixing during extraction from the mantle is a key process for controlling the trace element and isotope variability observed in basaltic lavas and must be evaluated before inferring the presence of multiple source component

τ→ρππν\tau\to\rho\pi\pi\nu decays

Effective chiral theory of mesons is applied to study the four decay modes of $\tau\to\rho\pi\pi\nu$. Theoretical values of the branching ratios are in agreement with the data. The theory predicts that the $a_{1}$ resonance plays a dominant role in these decays. There is no new parameter in this study.Comment: 12 pages and one figur

Probing photo-ionization: simulations of positive streamers in varying N2:O2 mixtures

Photo-ionization is the accepted mechanism for the propagation of positive streamers in air though the parameters are not very well known; the efficiency of this mechanism largely depends on the presence of both nitrogen and oxygen. But experiments show that streamer propagation is amazingly robust against changes of the gas composition; even for pure nitrogen with impurity levels below 1 ppm streamers propagate essentially with the same velocity as in air, but their minimal diameter is smaller, and they branch more frequently. Additionally, they move more in a zigzag fashion and sometimes exhibit a feathery structure. In our simulations, we test the relative importance of photo-ionization and of the background ionization from pulsed repetitive discharges, in air as well as in nitrogen with 1 ppm O2 . We also test reasonable parameter changes of the photo-ionization model. We find that photo- ionization dominates streamer propagation in air for repetition frequencies of at least 1 kHz, while in nitrogen with 1 ppm O2 the effect of the repetition frequency has to be included above 1 Hz. Finally, we explain the feather-like structures around streamer channels that are observed in experiments in nitrogen with high purity, but not in air.Comment: 12 figure

Probing background ionization: Positive streamers with varying pulse repetition rate and with a radioactive admixture

Positive streamers need a source of free electrons ahead of them to propagate. A streamer can supply these electrons by itself through photo-ionization, or the electrons can be present due to external background ionization. Here we investigate the effects of background ionization on streamer propagation and morphology by changing the gas composition and the repetition rate of the voltage pulses, and by adding a small amount of radioactive Krypton 85. We find that the general morphology of a positive streamer discharge in high purity nitrogen depends on background ionization: at lower background ionization levels the streamers branch more and have a more feather-like appearance. This is observed both when varying the repetition rate and when adding Krypton 85, though side branches are longer with the radioactive admixture. But velocities and minimal diameters of streamers are virtually independent of the background ionization level. In air, the inception cloud breaks up into streamers at a smaller radius when the repetition rate and therefore the background ionization level is higher. When measuring the effects of the pulse repetition rate and of the radioactive admixture on the discharge morphology, we found that our estimates of background ionization levels are consistent with these observations; this gives confidence in the estimates. Streamer channels generally do not follow the paths of previous discharge channels for repetition rates of up to 10 Hz. We estimate the effect of recombination and diffusion of ions and free electrons from the previous discharge and conclude that the old trail has largely disappeared at the moment of the next voltage pulse; therefore the next streamers indeed cannot follow the old trail.Comment: 30 pages, 13 figure

Positive and negative streamers in ambient air: modeling evolution and velocities

We simulate short positive and negative streamers in air at standard temperature and pressure. They evolve in homogeneous electric fields or emerge from needle electrodes with voltages of 10 to 20 kV. The streamer velocity at given streamer length depends only weakly on the initial ionization seed, except in the case of negative streamers in homogeneous fields. We characterize the streamers by length, head radius, head charge and field enhancement. We show that the velocity of positive streamers is mainly determined by their radius and in quantitative agreement with recent experimental results both for radius and velocity. The velocity of negative streamers is dominated by electron drift in the enhanced field; in the low local fields of the present simulations, it is little influenced by photo-ionization. Though negative streamer fronts always move at least with the electron drift velocity in the local field, this drift motion broadens the streamer head, decreases the field enhancement and ultimately leads to slower propagation or even extinction of the negative streamer.Comment: 18 pages, 10 figure