Compression of quantum measurement operations

We generalize recent work of Massar and Popescu dealing with the amount of classical data that is produced by a quantum measurement on a quantum state ensemble. In the previous work it was shown how spurious randomness generally contained in the outcomes can be eliminated without decreasing the amount of knowledge, to achieve an amount of data equal to the von Neumann entropy of the ensemble. Here we extend this result by giving a more refined description of what constitute equivalent measurements (that is measurements which provide the same knowledge about the quantum state) and also by considering incomplete measurements. In particular we show that one can always associate to a POVM with elements a_j, an equivalent POVM acting on many independent copies of the system which produces an amount of data asymptotically equal to the entropy defect of an ensemble canonically associated to the ensemble average state and the initial measurement (a_j). In the case where the measurement is not maximally refined this amount of data is strictly less than the von Neumann entropy, as obtained in the previous work. We also show that this is the best achievable, i.e. it is impossible to devise a measurement equivalent to the initial measurement (a_j) that produces less data. We discuss the interpretation of these results. In particular we show how they can be used to provide a precise and model independent measure of the amount of knowledge that is obtained about a quantum state by a quantum measurement. We also discuss in detail the relation between our results and Holevo's bound, at the same time providing a new proof of this fundamental inequality.Comment: RevTeX, 13 page

Bonding in complexes of bis(pentalene)di-titanium, Ti2(C8H6)2

Bonding in the bis(pentalene)di-titanium ‘double-sandwich’ species Ti2Pn2 (Pn = C8H6) and its interaction with other fragments have been investigated by xdensity functional calculations and fragment analysis. Ti2Pn2 with C2v symmetry has two metal-metal bonds and a low-lying metal based empty orbital, all three frontier orbitals having a1 symmetry. The latter may be regarded as being derived by symmetric combinations of the classic three frontier orbitals of two bent bis(cyclopentadienyl) metal fragments. Electrochemical studies on Ti2Pn†2 (Pn† = C8H4{SiiPr3-1,4}2) reveal a one-electron oxidation, and the formally mixed-valence Ti(II)-Ti(III) cationic complex [Ti2Pn†2][B(C6F5)4] has been structurally characterised. Theory indicates an S = ½ ground state electronic configuration for the latter, confirmed by EPR spectroscopy and SQUID magnetometry. Carbon dioxide binds symmetrically to Ti2Pn2 preserving C2v symmetry, as does carbon disulfide. The dominant interaction in Ti2Pn2CO2 is σ donation into the LUMO of bent CO2 and donation from the O atoms to Ti2Pn2 is minimal, whereas in Ti2Pn2CS2 there is significant interaction with the S atoms. The bridging O atom in the mono(oxo) species Ti2Pn2O, however, employs all three O 2p orbitals in binding and competes strongly with Pn, leading to weaker binding of the carbocyclic ligand, and the sulfur analog Ti2Pn2S behaves similarly. Ti2Pn2 is also capable of binding one, two and three molecules of carbon monoxide. The bonding demands of a single CO molecule are incompatible with symmetric binding and an asymmetric structure is found. The dicarbonyl adduct Ti2Pn2(CO)2 has Cs symmetry with the Ti2Pn2 unit acting as two MCp2 fragments. Synthetic studies show, that in the presence of excess CO a tricarbonyl complex Ti2Pn†2(CO)3 is formed, which optimises to an asymmetric structure with two terminal CO ligands and one semi-bridging. Low temperature 13C NMR spectroscopy reveals a rapid dynamic exchange between the two bound CO sites and free CO

Information storing by biomagnetites

Since the discovery of the presence of biogenic magnetites in living organisms, there have been speculations on the role that these biomagnetites play in cellular processes. It seems that the formation of biomagnetite crystals is a universal phenomenon and not an exception in living cells. Many experimental facts show that features of organic and inorganic processes could be indistinguishable at nanoscale levels. Living cells are quantum "devices" rather than simple electronic devices utilizing only the charge of conduction electrons. In our opinion, due to their unusual biophysical properties, special biomagnetites must have a biological function in living cells in general and in the brain in particular. In this paper we advance a hypothesis that while biomagnetites are developed jointly with organic molecules and cellular electromagnetic fields in cells, they can record information about the Earth's magnetic vector potential of the entire flight in migratory birds.Comment: 17 pages, 3 figure

Finite Element Analysis of Bone and Experimental Validation

This chapter describes the application of the finite element (FE) method to bone tissues. The aspects that differ the most between bone and other materials’ FE analysis are the type of elements used, constitutive models, and experimental validation. These aspects are looked at from a historical evolution stand point. Several types of elements can be used to simulate similar bone structures and within the same analysis many types of elements may be needed to realistically simulate an anatomical part. Special attention is made to constitutive models, including the use of density-elasticity relationships made possible through CT-scanned images. Other more complex models are also described that include viscoelasticity and anisotropy. The importance of experimental validation is discussed, describing several methods used by different authors in this challenging field. The use of cadaveric human bones is not always possible or desirable and other options are described, as the use of animal or artificial bones. Strain and strain rate measuring methods are also discussed, such as rosette strain gauges and optical devices.publishe

Barriers to Predicting the Mechanisms and Risk Factors of Non-Contact Anterior Cruciate Ligament Injury

High incidences of non-contact anterior cruciate ligament (ACL) injury, frequent requirements for ACL reconstruction, and limited understanding of ACL mechanics have engendered considerable interest in quantifying the ACL loading mechanisms. Although some progress has been made to better understand non-contact ACL injuries, information on how and why non-contact ACL injuries occur is still largely unavailable. In other words, research is yet to yield consensus on injury mechanisms and risk factors. Biomechanics, video analysis, and related study approaches have elucidated to some extent how ACL injuries occur. However, these approaches are limited because they provide estimates, rather than precise measurements of knee - and more specifically ACL - kinematics at the time of injury. These study approaches are also limited in their inability to simultaneously capture many of the contributing factors to injury

Global fine-resolution data on springtail abundance and community structure

Springtails (Collembola) inhabit soils from the Arctic to the Antarctic and comprise an estimated ~32% of all terrestrial arthropods on Earth. Here, we present a global, spatially-explicit database on springtail communities that includes 249,912 occurrences from 44,999 samples and 2,990 sites. These data are mainly raw sample-level records at the species level collected predominantly from private archives of the authors that were quality-controlled and taxonomically-standardised. Despite covering all continents, most of the sample-level data come from the European continent (82.5% of all samples) and represent four habitats: woodlands (57.4%), grasslands (14.0%), agrosystems (13.7%) and scrublands (9.0%). We included sampling by soil layers, and across seasons and years, representing temporal and spatial within-site variation in springtail communities. We also provided data use and sharing guidelines and R code to facilitate the use of the database by other researchers. This data paper describes a static version of the database at the publication date, but the database will be further expanded to include underrepresented regions and linked with trait data.</p

Global fine-resolution data on springtail abundance and community structure

CODE AVAILABILITY : Programming R code is openly available together with the database from Figshare.SUPPLEMENTARY MATERIAL 1 : Template for data collectionSUPPLEMENTARY MATERIAL 2 : Data Descriptor WorksheetSpringtails (Collembola) inhabit soils from the Arctic to the Antarctic and comprise an estimated ~32% of all terrestrial arthropods on Earth. Here, we present a global, spatially-explicit database on springtail communities that includes 249,912 occurrences from 44,999 samples and 2,990 sites. These data are mainly raw sample-level records at the species level collected predominantly from private archives of the authors that were quality-controlled and taxonomically-standardised. Despite covering all continents, most of the sample-level data come from the European continent (82.5% of all samples) and represent four habitats: woodlands (57.4%), grasslands (14.0%), agrosystems (13.7%) and scrublands (9.0%). We included sampling by soil layers, and across seasons and years, representing temporal and spatial within-site variation in springtail communities. We also provided data use and sharing guidelines and R code to facilitate the use of the database by other researchers. This data paper describes a static version of the database at the publication date, but the database will be further expanded to include underrepresented regions and linked with trait data.Open Access funding enabled and organized by Projekt DEAL.http://www.nature.com/sdatahj2024Plant Production and Soil ScienceSDG-15:Life on lan