Single-copy entanglement in a gapped quantum spin chain

The single-copy entanglement of a given many-body system is defined [J. Eisert and M. Cramer, Phys. Rev. A. 72, 042112 (2005)] as the maximal entanglement deterministically distillable from a bipartition of a single specimen of that system. For critical (gapless) spin chains, it was recently shown that this is exactly half the von Neumann entropy [R. Orus, J. I. Latorre, J. Eisert, and M. Cramer, Phys. Rev. A 73, 060303(R) (2006)], itself defined as the entanglement distillable in the asymptotic limit: i.e. given an infinite number of copies of the system. It is an open question as to what the equivalent behaviour for gapped systems is. In this paper, I show that for the paradigmatic spin-S Affleck-Kennedy-Lieb-Tasaki chain (the archetypal gapped chain), the single-copy entanglement is equal to the von Neumann entropy: i.e. all the entanglement present may be distilled from a single specimen.Comment: Typos corrected; accepted for publication in Phys. Rev. Lett.; comments welcom

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VLBI observations of SN 2008iz: I. Expansion velocity and limits on anisotropic expansion

We present observations of the recently discovered supernova 2008iz in M82 with the VLBI High Sensitivity Array at 22 GHz, the Very Large Array at frequencies of 1.4, 4.8, 8.4, 22 and 43 GHz, and the Chandra X-ray observatory. The supernova was clearly detected on two VLBI images, separated by 11 months. The source shows a ring-like morphology and expands with a velocity of ~23000 km/s. The most likely explosion date is in mid February 2008. The measured expansion speed is a factor of ~2 higher than expected under the assumption that synchrotron self-absorption dominates the light curve at the peak, indicating that this absorption mechanism may not be important for the radio emission. We find no evidence for an asymmetric explosion. The VLA spectrum shows a broken power law, indicating that the source was still optically thick at 1.4 GHz in April 2009. Finally, we report upper limits on the X-ray emission from SN 2008iz and a second radio transient recently discovered by MERLIN observations.Comment: accepted Astronomy & Astrophysics, 9 pages, 8 figures, also available at http://www.mpifr-bonn.mpg.de/staff/abrunthaler/pub.shtm

8.4GHz VLBI observations of SN2004et in NGC6946

We report on 8.4GHz Very Long Baseline Interferometry (VLBI) observations of the type II-P supernova SN2004et in the spiral galaxy NGC 6946, made on 20 February 2005 (151 days after explosion). The Very Large Array (VLA) flux density was 1.23$\pm$0.07 mJy, corresponding to an isotropic luminosity at 8.4GHz of (4.45$\pm$0.3)$\times10^{25}$ erg s$^{-1}$ Hz$^{-1}$ and a brightness temperature of (1.3$\pm$0.3)$\times10^{8}$ K. We also provide an improved source position, accurate to about 0.5 mas in each coordinate. The VLBI image shows a clear asymmetry. From model fitting of the size of the radio emission, we estimate a minimum expansion velocity of 15,700$\pm$2,000 km s$^{-1}$. This velocity is more than twice the expected mean expansion velocity estimated from a synchrotron self-absorbed emission model, thus suggesting that synchrotron self-absorption is not relevant for this supernova. With the benefit of an optical spectrum obtained 12 days after explosion, we favor an emission model which consists of two hot spots on an underlying expanding shell of width comparable to that of SN 1993J.Comment: Accepted for publication in A&A (22/05/07

The nuclear starburst in Arp 299-A: From the 5.0 GHz VLBI radio light-curves to its core-collapse supernova rate

The nuclear region of the Luminous Infra-red Galaxy Arp 299-A hosts a recent ($\simeq 10$ Myr), intense burst of massive star formation which is expected to lead to numerous core-collapse supernovae (CCSNe). Previous VLBI observations, carried out with the EVN at 5.0 GHz and with the VLBA at 2.3 and 8.4 GHz, resulted in the detection of a large number of compact, bright, non-thermal sources in a region \lsim150 pc in size. We aim at establishing the nature of all non-thermal, compact components in Arp 299-A, as well as estimating its core-collapse supernova rate. We use multi-epoch European VLBI Network (EVN) observations taken at 5.0 GHz to image with milliarcsecond resolution the compact radio sources in the nuclear region of Arp 299-A. We also use one single-epoch 5.0 GHz Multi-Element Radio Linked Interferometer Network (MERLIN) observation to image the extended emission in which the compact radio sources --traced by our EVN observations-- are embedded. Twenty-six compact sources are detected, 8 of them are new objects not previously detected. The properties of all detected objects are consistent with them being a mixed population of CCSNe and SNRs. We find clear evidence for at least two new CCSNe, implying a lower limit to the CCSN rate of \nu_{\rm SN}\gsim0.80 SN/yr indicating that the bulk of the current star formation in Arp 299-A is taking place in the innermost $\sim 150$ pc. Our MERLIN observations trace a region of diffuse, extended emission which is co-spatial to the region where all compact sources are found. From this diffuse, non-thermal radio emission we obtain an independent estimate for the core-collapse supernova rate, which is in the range $\nu_{\rm SN}=0.40$ - 0.65 SN/yr, roughly in agreement with previous estimates and our direct estimate of the CCSN rate from the compact radio emission.Comment: 13 pages, 5 figures, accepted for publication on Astronomy & Astrophysic

Further results on the cross norm criterion for separability

In the present paper the cross norm criterion for separability of density matrices is studied. In the first part of the paper we determine the value of the greatest cross norm for Werner states, for isotropic states and for Bell diagonal states. In the second part we show that the greatest cross norm criterion induces a novel computable separability criterion for bipartite systems. This new criterion is a necessary but in general not a sufficient criterion for separability. It is shown, however, that for all pure states, for Bell diagonal states, for Werner states in dimension d=2 and for isotropic states in arbitrary dimensions the new criterion is necessary and sufficient. Moreover, it is shown that for Werner states in higher dimensions (d greater than 2), the new criterion is only necessary.Comment: REVTeX, 19 page

23 GHz VLBI Observations of SN 2008ax

We report on phase-referenced 23 GHz Very-Long-Baseline-Interferometry (VLBI) observations of the type IIb supernova SN 2008ax, made with the Very Long Baseline Array (VLBA) on 2 April 2008 (33 days after explosion). These observations resulted in a marginal detection of the supernova. The total flux density recovered from our VLBI image is 0.8$\pm$0.3 mJy (one standard deviation). As it appears, the structure may be interpreted as either a core-jet or a double source. However, the supernova structure could be somewhat confused with a possible close by noise peak. In such a case, the recovered flux density would decrease to 0.48$\pm$0.12 mJy, compatible with the flux densities measured with the VLA at epochs close in time to our VLBI observations. The lowest average expansion velocities derived from our observations are $(1.90 \pm 0.30) \times 10^5$ km s$^{-1}$ (case of a double source) and $(5.2 \pm 1.3) \times 10^4$ km s$^{-1}$ (taking the weaker source component as a spurious, close by, noise peak, which is the more likely interpretation). These velocities are 7.3 and 2 times higher, respectively, than the maximum ejecta velocity inferred from optical-line observations.Comment: 4 pages, 3 figures. Accepted in A&A on 24/03/200

The impact of Charlson comorbidity index on the functional capacity of COVID-19 survivors: a prospective cohort study with one-year follow-up

Objective: To determine the association between the Charlson comorbidity index (CCI) score after discharge with 6-min walk test (6MWT) 1 year after discharge in a cohort of COVID-19 survivors. Methods: In this prospective study, data were collected from a consecutive sample of patients hospitalized for COVID-19. The CCI score was calculated from the comorbidity data. The main outcome was the distance walked in the 6MWT at 1 year after discharge. Associations between CCI and meters covered in the 6MWT were assessed through crude and adjusted linear regressions. The model was adjusted for possible confounding factors (sex, days of hospitalization, and basal physical capacity through sit-to-stand test one month after discharge). Results: A total of 41 patients were included (mean age 58.8 +/- 12.7 years, 20/21 men/women). A significant association was observed between CCI and 6MWT (meters): (i) crude model: beta = -18.7, 95% CI = -34.7 to -2.6, p < 0.05; (ii) model adjusted for propensity score including sex, days of hospitalization, and sit-to-stand: beta = -23.0, 95% CI = -39.1 to -6.8, p < 0.05. Conclusions: A higher CCI score after discharge indicates worse performance on the 6MWT at 1-year follow-up in COVID-19 survivors. The CCI score could also be used as a screening tool to make important clinical decisions