de Finetti reductions for correlations

When analysing quantum information processing protocols one has to deal with large entangled systems, each consisting of many subsystems. To make this analysis feasible, it is often necessary to identify some additional structure. de Finetti theorems provide such a structure for the case where certain symmetries hold. More precisely, they relate states that are invariant under permutations of subsystems to states in which the subsystems are independent of each other. This relation plays an important role in various areas, e.g., in quantum cryptography or state tomography, where permutation invariant systems are ubiquitous. The known de Finetti theorems usually refer to the internal quantum state of a system and depend on its dimension. Here we prove a different de Finetti theorem where systems are modelled in terms of their statistics under measurements. This is necessary for a large class of applications widely considered today, such as device independent protocols, where the underlying systems and the dimensions are unknown and the entire analysis is based on the observed correlations.Comment: 5+13 pages; second version closer to the published one; new titl

Free energy density for mean field perturbation of states of a one-dimensional spin chain

Motivated by recent developments on large deviations in states of the spin chain, we reconsider the work of Petz, Raggio and Verbeure in 1989 on the variational expression of free energy density in the presence of a mean field type perturbation. We extend their results from the product state case to the Gibbs state case in the setting of translation-invariant interactions of finite range. In the special case of a locally faithful quantum Markov state, we clarify the relation between two different kinds of free energy densities (or pressure functions).Comment: 29 pages, Section 5 added, to appear in Rev. Math. Phy

Monogamy of entanglement and other correlations

It has been observed by numerous authors that a quantum system being entangled with another one limits its possible entanglement with a third system: this has been dubbed the "monogamous nature of entanglement". In this paper we present a simple identity which captures the trade-off between entanglement and classical correlation, which can be used to derive rigorous monogamy relations. We also prove various other trade-offs of a monogamy nature for other entanglement measures and secret and total correlation measures.Comment: 7 pages, revtex

Monogamy of Correlations vs. Monogamy of Entanglement

A fruitful way of studying physical theories is via the question whether the possible physical states and different kinds of correlations in each theory can be shared to different parties. Over the past few years it has become clear that both quantum entanglement and non-locality (i.e., correlations that violate Bell-type inequalities) have limited shareability properties and can sometimes even be monogamous. We give a self-contained review of these results as well as present new results on the shareability of different kinds of correlations, including local, quantum and no-signalling correlations. This includes an alternative simpler proof of the Toner-Verstraete monogamy inequality for quantum correlations, as well as a strengthening thereof. Further, the relationship between sharing non-local quantum correlations and sharing mixed entangled states is investigated, and already for the simplest case of bi-partite correlations and qubits this is shown to be non-trivial. Also, a recently proposed new interpretation of Bell's theorem by Schumacher in terms of shareability of correlations is critically assessed. Finally, the relevance of monogamy of non-local correlations for secure quantum key distribution is pointed out, although, and importantly, it is stressed that not all non-local correlations are monogamous.Comment: 12 pages, 2 figures. Invited submission to a special issue of Quantum Information Processing. v2: Published version. Open acces

Notes on entropic characteristics of quantum channels

One of most important issues in quantum information theory concerns transmission of information through noisy quantum channels. We discuss few channel characteristics expressed by means of generalized entropies. Such characteristics can often be dealt in line with more usual treatment based on the von Neumann entropies. For any channel, we show that the $q$-average output entropy of degree $q\geq1$ is bounded from above by the $q$-entropy of the input density matrix. Concavity properties of the $(q,s)$-entropy exchange are considered. Fano type quantum bounds on the $(q,s)$-entropy exchange are derived. We also give upper bounds on the map $(q,s)$-entropies in terms of the output entropy, corresponding to the completely mixed input.Comment: 10 pages, no figures. The statement of Proposition 1 is explicitly illustrated with the depolarizing channel. The bibliography is extended and updated. More explanations. To be published in Cent. Eur. J. Phy

Faithful Squashed Entanglement

Squashed entanglement is a measure for the entanglement of bipartite quantum states. In this paper we present a lower bound for squashed entanglement in terms of a distance to the set of separable states. This implies that squashed entanglement is faithful, that is, strictly positive if and only if the state is entangled. We derive the bound on squashed entanglement from a bound on quantum conditional mutual information, which is used to define squashed entanglement and corresponds to the amount by which strong subadditivity of von Neumann entropy fails to be saturated. Our result therefore sheds light on the structure of states that almost satisfy strong subadditivity with equality. The proof is based on two recent results from quantum information theory: the operational interpretation of the quantum mutual information as the optimal rate for state redistribution and the interpretation of the regularised relative entropy of entanglement as an error exponent in hypothesis testing. The distance to the set of separable states is measured by the one-way LOCC norm, an operationally-motivated norm giving the optimal probability of distinguishing two bipartite quantum states, each shared by two parties, using any protocol formed by local quantum operations and one-directional classical communication between the parties. A similar result for the Frobenius or Euclidean norm follows immediately. The result has two applications in complexity theory. The first is a quasipolynomial-time algorithm solving the weak membership problem for the set of separable states in one-way LOCC or Euclidean norm. The second concerns quantum Merlin-Arthur games. Here we show that multiple provers are not more powerful than a single prover when the verifier is restricted to one-way LOCC operations thereby providing a new characterisation of the complexity class QMA.Comment: 24 pages, 1 figure, 1 table. Due to an error in the published version, claims have been weakened from the LOCC norm to the one-way LOCC nor

Prevalence of dental caries in preschool children by ICDAS diagnostic methodology

Objective: To evaluate the prevalence of caries with the ICDAS index (International Caries Detection and Assessment System) using different cut-off points in children from public and private institutions as well as to associate the presence of caries with socioeconomic indicators, sex, age, type of school (urban or rural) and also family health program with dentist's presence at the school. Material and Methods: An analytical cross-sectional study with a stratified sample (n = 612) in children ranging from three to six years old, in public and private institutions of the city of Barras, State of Piaui, Brazil. The clinical examination was based on ICDAS criteria, and a questionnaire for socioeconomic and educational level data was also applied. Different cut-off points were used, as follows: cut-off point 1 (scores 0 and 1 considered as healthy and scores 2-6 classified as decayed); cut-off point 2 (scores from 0 to 2 classified as healthy, scores 3 to 6 as decayed) and cut-off point 3 (0 to 3 healthy, 4 to 6 decayed). Univariate and Multiple Poisson regression analysis were performed, with 5% significance level. Results: For cut-off point 1, the prevalence was 68.8%; Cut-off point 2, 67.9% and at the cut-off point 3, 60.6%. An association was found in the prevalence of caries with the child's age (p = 0.004), school zone (urban or rural) (p = 0.004) and the presence of the dentist at school (p = 0.001). Conclusion: Taking into account the various cut-off points, the prevalence of caries in preschool children was considered high. The presence of caries lesions is more likely to occur in five year- old boys living in the countryside

Study Protocol for an Online Questionnaire Survey on Symptoms/Signs, Protective Measures, Level of Awareness and Perception Regarding COVID-19 Outbreak among Dentists. A Global Survey

The Centres for Disease Control and Prevention and the World Health Organization have developed preparedness and prevention checklists for healthcare professionals regarding the containment of COVID-19. The aim of the present protocol is to evaluate the impact of the COVID-19 outbreak among dentists in different countries where various prevalence of the epidemic has been reported. Several research groups around the world were contacted by the central management team. The online anonymous survey will be conducted on a convenience sample of dentists working both in national health systems and in private or public clinics. In each country/area, a high (~5–20%) proportion of dentists working there will be invited to participate. The questionnaire, developed and standardized previously in Italy, has four domains: (1) personal data; (2) symptoms/signs relative to COVID-19; (3) working conditions and PPE (personal protective equipment) adopted after the infection’s outbreak; (4) knowledge and self-perceived risk of infection. The methodology of this international survey will include translation, pilot testing, and semantic adjustment of the questionnaire. The data will be entered on an Excel spreadsheet and quality checked. Completely anonymous data analyses will be performed by the central management team. This survey will give an insight into the dental profession during COVID-19 pandemic globally

High-precision measurements of low-lying isomeric states in 120−124^{120-124}In with JYFLTRAP double Penning trap

Neutron-rich $^{120-124}$In isotopes have been studied utilizing the double Penning trap mass spectrometer JYFLTRAP at the IGISOL facility. Using the phase-imaging ion-cyclotron-resonance technique, the isomeric states were resolved from ground states and their excitation energies measured with high precision in $^{121,123,124}$In. In $^{120,122}$In, the $1^+$ states were separated and their masses were measured while the energy difference between the unresolved $5^+$ and $8^-$ states, whose presence was confirmed by post-trap decay spectroscopy was determined to be $\leq15$ keV. In addition, the half-life of $^{122}$Cd, $T_{1/2} = 5.98(10)$ s, was extracted. Experimental results were compared with energy density functionals, density functional theory and shell-model calculations.Comment: 11 pages, 7 figure