The Gravity Dual of a Density Matrix

For a state in a quantum field theory on some spacetime, we can associate a density matrix to any subset of a given spacelike slice by tracing out the remaining degrees of freedom. In the context of the AdS/CFT correspondence, if the original state has a dual bulk spacetime with a good classical description, it is natural to ask how much information about the bulk spacetime is carried by the density matrix for such a subset of field theory degrees of freedom. In this note, we provide several constraints on the largest region that can be fully reconstructed, and discuss specific proposals for the geometric construction of this dual region.Comment: 19 pages, LaTeX, 8 figures, v2: footnote and reference adde

Range-wide sources of variation in reproductive rates of northern spotted owls

We conducted a range-wide investigation of the dynamics of site-level reproductive rate of northern spotted owls using survey data from 11 study areas across the subspecies geographic range collected during 1993–2018. Our analytical approach accounted for imperfect detection of owl pairs and misclassification of successful reproduction (i.e., at least one young fledged) and contributed further insights into northern spotted owl population ecology and dynamics. Both nondetection and state misclassification were important, especially because factors affecting these sources of error also affected focal ecological parameters. Annual probabilities of site occupancy were greatest at sites with successful reproduction in the previous year and lowest for sites not occupied by a pair in the previous year. Site-specific occupancy transition probabilities declined over time and were negatively affected by barred owl presence. Overall, the site-specific probability of successful reproduction showed substantial year-to-year fluctuations and was similar for occupied sites that did or did not experience successful reproduction the previous year. Site-specific probabilities for successful reproduction were very small for sites that were unoccupied the previous year. Barred owl presence negatively affected the probability of successful reproduction by northern spotted owls in Washington and California, as predicted, but the effect in Oregon was mixed. The proportions of sites occupied by northern spotted owl pairs showed steep, near-monotonic declines over the study period, with all study areas showing the lowest observed levels of occupancy to date. If trends continue it is likely that northern spotted owls will become extirpated throughout large portions of their range in the coming decades