Bose-Fermi duality and entanglement entropies

Entanglement (Renyi) entropies of spatial regions are a useful tool for characterizing the ground states of quantum field theories. In this paper we investigate the extent to which these are universal quantities for a given theory, and to which they distinguish different theories, by comparing the entanglement spectra of the massless Dirac fermion and the compact free boson in two dimensions. We show that the calculation of Renyi entropies via the replica trick for any orbifold theory includes a sum over orbifold twists on all cycles. In a modular-invariant theory of fermions, this amounts to a sum over spin structures. The result is that the Renyi entropies respect the standard Bose-Fermi duality. Next, we investigate the entanglement spectrum for the Dirac fermion without a sum over spin structures, and for the compact boson at the self-dual radius. These are not equivalent theories; nonetheless, we find that (1) their second Renyi entropies agree for any number of intervals, (2) their full entanglement spectra agree for two intervals, and (3) the spectrum generically disagrees otherwise. These results follow from the equality of the partition functions of the two theories on any Riemann surface with imaginary period matrix. We also exhibit a map between the operators of the theories that preserves scaling dimensions (but not spins), as well as OPEs and correlators of operators placed on the real line. All of these coincidences can be traced to the fact that the momentum lattice for the bosonized fermion is related to that of the self-dual boson by a 45 degree rotation that mixes left- and right-movers.Comment: 40 pages; v3: improvements to presentation, new section discussing entanglement negativit

Generation of Three-Qubit Entangled States using Superconducting Phase Qubits

Entanglement is one of the key resources required for quantum computation, so experimentally creating and measuring entangled states is of crucial importance in the various physical implementations of a quantum computer. In superconducting qubits, two-qubit entangled states have been demonstrated and used to show violations of Bell's Inequality and to implement simple quantum algorithms. Unlike the two-qubit case, however, where all maximally-entangled two-qubit states are equivalent up to local changes of basis, three qubits can be entangled in two fundamentally different ways, typified by the states $|\mathrm{GHZ}> = (|000> + |111>)/\sqrt{2}$ and $|\mathrm{W}> = (|001> + |010> + |100>)/\sqrt{3}$. Here we demonstrate the operation of three coupled superconducting phase qubits and use them to create and measure $|\mathrm{GHZ}>$ and $|\mathrm{W}>$ states. The states are fully characterized using quantum state tomography and are shown to satisfy entanglement witnesses, confirming that they are indeed examples of three-qubit entanglement and are not separable into mixtures of two-qubit entanglement.Comment: 9 pages, 5 figures. Version 2: added supplementary information and fixed image distortion in Figure 2

Recurrent mutation of IGF signalling genes and distinct patterns of genomic rearrangement in osteosarcoma

Osteosarcoma is a primary malignancy of bone that affects children and adults. Here, we present the largest sequencing study of osteosarcoma to date, comprising 112 childhood and adult tumours encompassing all major histological subtypes. A key finding of our study is the identification of mutations in insulin-like growth factor (IGF) signalling genes in 8/112 (7%) of cases. We validate this observation using fluorescence in situ hybridization (FISH) in an additional 87 osteosarcomas, with IGF1 receptor (IGF1R) amplification observed in 14% of tumours. These findings may inform patient selection in future trials of IGF1R inhibitors in osteosarcoma. Analysing patterns of mutation, we identify distinct rearrangement profiles including a process characterized by chromothripsis and amplification. This process operates recurrently at discrete genomic regions and generates driver mutations. It may represent an age-independent mutational mechanism that contributes to the development of osteosarcoma in children and adults alike

Emulating Natural Disturbances for Declining Late- Successional Species: A Case Study of the Consequences for Cerulean Warblers (Setophaga cerulea)

Forest cover in the eastern United States has increased over the past century and while some late-successional species have benefited from this process as expected, others have experienced population declines. These declines may be in part related to contemporary reductions in small-scale forest interior disturbances such as fire, windthrow, and treefalls. To mitigate the negative impacts of disturbance alteration and suppression on some late-successional species, strategies that emulate natural disturbance regimes are often advocated, but large-scale evaluations of these practices are rare. Here, we assessed the consequences of experimental disturbance (using partial timber harvest) on a severely declining late-successional species, the cerulean warbler (Setophaga cerulea), across the core of its breeding range in the Appalachian Mountains. We measured numerical (density), physiological (body condition), and demographic (age structure and reproduction) responses to three levels of disturbance and explored the potential impacts of disturbance on source-sink dynamics. Breeding densities of warblers increased one to four years after all canopy disturbances (vs. controls) and males occupying territories on treatment plots were in better condition than those on control plots. However, these beneficial effects of disturbance did not correspond to improvements in reproduction; nest success was lower on all treatment plots than on control plots in the southern region and marginally lower on light disturbance plots in the northern region. Our data suggest that only habitats in the southern region acted as sources, and interior disturbances in this region have the potential to create ecological traps at a local scale, but sources when viewed at broader scales. Thus, cerulean warblers would likely benefit from management that strikes a landscape-level balance between emulating natural disturbances in order to attract individuals into areas where current structure is inappropriate, and limiting anthropogenic disturbance in forests that already possess appropriate structural attributes in order to maintain maximum productivity

Emulating Natural Disturbances for Declining Late-Successional Species: A Case Study of the Consequences for Cerulean Warblers (Setophaga cerulea)

Forest cover in the eastern United States has increased over the past century and while some late-successional species have benefited from this process as expected, others have experienced population declines. These declines may be in part related to contemporary reductions in small-scale forest interior disturbances such as fire, windthrow, and treefalls. To mitigate the negative impacts of disturbance alteration and suppression on some late-successional species, strategies that emulate natural disturbance regimes are often advocated, but large-scale evaluations of these practices are rare. Here, we assessed the consequences of experimental disturbance (using partial timber harvest) on a severely declining latesuccessional species, the cerulean warbler (Setophaga cerulea), across the core of its breeding range in the Appalachian Mountains. We measured numerical (density), physiological (body condition), and demographic (age structure and reproduction) responses to three levels of disturbance and explored the potential impacts of disturbance on source-sink dynamics. Breeding densities of warblers increased one to four years after all canopy disturbances (vs. controls) and males occupying territories on treatment plots were in better condition than those on control plots. However, these beneficial effects of disturbance did not correspond to improvements in reproduction; nest success was lower on all treatment plots than on control plots in the southern region and marginally lower on light disturbance plots in the northern region. Our data suggest that only habitats in the southern region acted as sources, and interior disturbances in this region have the potential to create ecological traps at a local scale, but sources when viewed at broader scales. Thus, cerulean warblers would likely benefit from management that strikes a landscape-level balance between emulating natural disturbances in order to attract individuals into areas where current structure is inappropriate, and limiting anthropogenic disturbance in forests that already possess appropriate structural attributes in order to maintain maximum productivity

Mechanistically-guided materials chemistry: synthesis of new ternary nitrides, CaZrN2_2 and CaHfN2_2

Recent computational studies have predicted many new ternary nitrides, revealing synthetic opportunities in this underexplored phase space. However, synthesizing new ternary nitrides is difficult, in part because intermediate and product phases often have high cohesive energies that inhibit diffusion. Here, we report the synthesis of two new phases, calcium zirconium nitride (CaZrN$_2$) and calcium hafnium nitride (CaHfN$_2$), by solid state metathesis reactions between Ca$_3$N$_2$ and $M$Cl$_4$ ($M$ = Zr, Hf). Although the reaction nominally proceeds to the target phases in a 1:1 ratio of the precursors via Ca$_3$N$_2$ + $M$Cl$_4$ $\rightarrow$ Ca$M$N$_2$ + 2 CaCl$_2$, reactions prepared this way result in Ca-poor materials (Ca$_xM_{2-x}$N$_2$, $x<1$). A small excess of Ca$_3$N$_2$ (ca. 20 mol\%) is needed to yield stoichiometric Ca$M$N$_2$, as confirmed by high-resolution synchrotron powder X-ray diffraction. In situ synchrotron X-ray diffraction studies reveal that nominally stoichiometric reactions produce Zr$^{3+}$ intermediates early in the reaction pathway, and the excess Ca$_3$N$_2$ is needed to reoxidize Zr$^{3+}$ intermediates back to the Zr$^{4+}$ oxidation state of CaZrN$_2$. Analysis of computationally-derived chemical potential diagrams rationalizes this synthetic approach and its contrast from the synthesis of MgZrN$_2$. These findings additionally highlight the utility of in situ diffraction studies and computational thermochemistry to provide mechanistic guidance for synthesis