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A fibre bundle structure is introduced over manifolds of quantum channels. This structure has a close connection with the problem of estimating an unknown quantum channel Γθ specified by a parameter θ. It is shown that the quantum Fisher information of the family of output states maximized over all input states , which quantifies the ultimate statistical distinguishability of the parameter θ, is expressed in terms of a geometrical quantity on the fibre bundle. Using this formula, a criterion for the maximum quantum Fisher information of the nth extended channel (id ⊗ Γθ)⊗n to be O(n) is derived. This criterion further proves that for almost all quantum channels, the maximum quantum Fisher information increases in the order of O(n).

We report phase-referencing VLBA observations of H 2 O masers near the starforming region W3(OH) to measure their parallax and absolute proper motions. The measured annual parallax is 0.489 ± 0.017 milli-arcseconds (2.04 ± 0.07 kpc), where the error is dominated by a systematic atmospheric contribution. This distance is consistent with photometric distances from previous observations and with the distance determined from CH 3 OH maser astrometry presented in a related paper. We also find that the source driving the H 2 O outflow, the "TW-object", moves with a 3-dimensional velocity of > 7 km s −1 relative to the ultracompact H II region W3(OH).

Evolved stars of about one solar mass are in general spherically symmetric, yet the planetary nebulae that they produce in the next phase of their evolution tend not to exhibit such symmetry. Collimated 'jets' and outflows of material have been observed up to approximately 0.3 parsec from the central stars of planetary nebulae, and precession of those jets has been proposed to explain the observed asymmetries. Moreover, it has recently been shown theoretically that magnetic fields could launch and collimate such jets. Here we report the detection of a collimated and precessing jet of molecular gas that is traced by water-vapour maser spots approximately 500 astronomical units (au) from the star W43A in Aquila. We conclude that the jet is formed in the immediate vicinity of the star, and infer that elongated planetary nebulae are formed by jets during the short period, of less than 1,000 years, when the star makes its transition through the proto-planetary nebula phase to become a planetary nebula.

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Planetary nebulae often have asymmetric shapes, even though their progenitor stars were symmetric; this structure could be the result of collimated jets from the evolved stars before they enter the planetary nebula phase. Theoretical models have shown that magnetic fields could be the dominant source of jet-collimation in evolved stars, just as these fields are thought to collimate outflows in other astrophysical sources, such as active galactic nuclei and proto-stars. But hitherto there have been no direct observations of both the magnetic field direction and strength in any collimated jet. Here we report measurements of the polarization of water vapour masers that trace the precessing jet emanating from the asymptotic giant branch star W43A (at a distance of 2.6 kpc from the Sun), which is undergoing rapid evolution into a planetary nebula. The masers occur in two clusters at opposing tips of the jets, approximately 1,000 au from the star. We conclude from the data that the magnetic field is indeed collimating the jet.

We present the results of our survey of 1612 MHz circumstellar OH maser emission from asymptotic giant branch (AGB) stars and red supergiants (RSGs) in the Large Magellanic Cloud. We have discovered four new circumstellar maser sources in the LMC, and increased the number of reliable wind speeds from IR stars in the LMC from 5 to 13. Using our new wind speeds, as well as those from Galactic sources, we have derived an updated relation for dust driven winds: v exp ∝ ZL 0.4 . We compare the sub-solar metallicity LMC OH/IR stars with carefully selected samples of more metal-rich OH/IR stars, also at known distances, in the Galactic Centre and Galactic Bulge. For 8 of the Bulge stars we derive pulsation periods for the first time, using near-IR photometry from the VVV survey. We have modeled our LMC OH/IR stars and developed an empirical method of deriving gas-to-dust ratios and mass loss rates by scaling the models to the results from maser profiles. We have done this also for samples in the Galactic Centre and Bulge and derived a new mass loss prescription that includes luminosity, pulsation period, and gas-to-dust ra-tioṀ = 1.06 +3.5 −0.8 ·10 −5 (L/10 4 L ) 0.9±0.1 (P/500 d) 0.75±0.3 (r gd /200) −0.03±0.07 M yr −1 . The tightest correlation is found between mass loss rate and luminosity. We find that the gas-to-dust ratio has little effect on the mass loss of oxygen-rich AGB stars and RSGs within the Galaxy and the LMC. This suggests that mass loss of oxygen-rich AGB stars and RSGs is (nearly) independent of metallicity between a half and twice solar.

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