Experimental implementation of a NMR entanglement witness

Entanglement witnesses (EW) allow the detection of entanglement in a quantum system, from the measurement of some few observables. They do not require the complete determination of the quantum state, which is regarded as a main advantage. On this paper it is experimentally analyzed an entanglement witness recently proposed in the context of Nuclear Magnetic Resonance (NMR) experiments to test it in some Bell-diagonal states. We also propose some optimal entanglement witness for Bell-diagonal states. The efficiency of the two types of EW's are compared to a measure of entanglement with tomographic cost, the generalized robustness of entanglement. It is used a GRAPE algorithm to produce an entangled state which is out of the detection region of the EW for Bell-diagonal states. Upon relaxation, the results show that there is a region in which both EW fails, whereas the generalized robustness still shows entanglement, but with the entanglement witness proposed here with a better performance

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

Correcting the spectroscopic surface gravity using transits and asteroseismology. No significant effect on temperatures or metallicities with ARES+MOOG in LTE

Precise stellar parameters are crucial for several reasons, amongst which are the precise characterization of orbiting exoplanets and the correct determination of galactic chemical evolution. The atmospheric parameters are extremely important because all the other stellar parameters depend on them. Using our standard equivalent-width method on high-resolution spectroscopy, good precision can be obtained for the derived effective temperature and metallicity. The surface gravity, however, is usually not well constrained with spectroscopy. We use two different samples of FGK dwarfs to study the effect of the stellar surface gravity on the precise spectroscopic determination of the other atmospheric parameters. Furthermore, we present a straightforward formula for correcting the spectroscopic surface gravities derived by our method and with our linelists. Our spectroscopic analysis is based on Kurucz models in LTE, performed with the MOOG code to derive the atmospheric parameters. The surface gravity was either left free or fixed to a predetermined value. The latter is either obtained through a photometric transit light curve or derived using asteroseismology. We find first that, despite some minor trends, the effective temperatures and metallicities for FGK dwarfs derived with the described method and linelists are, in most cases, only affected within the errorbars by using different values for the surface gravity, even for very large differences in surface gravity, so they can be trusted. The temperatures derived with a fixed surface gravity continue to be compatible within 1 sigma with the accurate results of the InfraRed Flux Method (IRFM), as is the case for the unconstrained temperatures. Secondly, we find that the spectroscopic surface gravity can easily be corrected to a more accurate value using a linear function with the effective temperature.Comment: 14 pages, 7 figures, 2 tables, accepted for publication in A&

A Generalization of Quantum Stein's Lemma

We present a generalization of quantum Stein's Lemma to the situation in which the alternative hypothesis is formed by a family of states, which can moreover be non-i.i.d.. We consider sets of states which satisfy a few natural properties, the most important being the closedness under permutations of the copies. We then determine the error rate function in a very similar fashion to quantum Stein's Lemma, in terms of the quantum relative entropy. Our result has two applications to entanglement theory. First it gives an operational meaning to an entanglement measure known as regularized relative entropy of entanglement. Second, it shows that this measure is faithful, being strictly positive on every entangled state. This implies, in particular, that whenever a multipartite state can be asymptotically converted into another entangled state by local operations and classical communication, the rate of conversion must be non-zero. Therefore, the operational definition of multipartite entanglement is equivalent to its mathematical definition.Comment: 30 pages. (see posting by M. Piani arXiv:0904.2705 for a different proof of the strict positiveness of the regularized relative entropy of entanglement on every entangled state). published version

Geometrically induced singular behavior of entanglement

We show that the geometry of the set of quantum states plays a crucial role in the behavior of entanglement in different physical systems. More specifically it is shown that singular points at the border of the set of unentangled states appear as singularities in the dynamics of entanglement of smoothly varying quantum states. We illustrate this result by implementing a photonic parametric down conversion experiment. Moreover, this effect is connected to recently discovered singularities in condensed matter models.Comment: v2: 4 pags, 4 figs. A discussion before the proof of Proposition 1 and tomographic results were included, Propostion 2 was removed and the references were fixe

Exponential Decay of Correlations Implies Area Law

We prove that a finite correlation length, i.e. exponential decay of correlations, implies an area law for the entanglement entropy of quantum states defined on a line. The entropy bound is exponential in the correlation length of the state, thus reproducing as a particular case Hastings proof of an area law for groundstates of 1D gapped Hamiltonians. As a consequence, we show that 1D quantum states with exponential decay of correlations have an efficient classical approximate description as a matrix product state of polynomial bond dimension, thus giving an equivalence between injective matrix product states and states with a finite correlation length. The result can be seen as a rigorous justification, in one dimension, of the intuition that states with exponential decay of correlations, usually associated with non-critical phases of matter, are simple to describe. It also has implications for quantum computing: It shows that unless a pure state quantum computation involves states with long-range correlations, decaying at most algebraically with the distance, it can be efficiently simulated classically. The proof relies on several previous tools from quantum information theory - including entanglement distillation protocols achieving the hashing bound, properties of single-shot smooth entropies, and the quantum substate theorem - and also on some newly developed ones. In particular we derive a new bound on correlations established by local random measurements, and we give a generalization to the max-entropy of a result of Hastings concerning the saturation of mutual information in multiparticle systems. The proof can also be interpreted as providing a limitation on the phenomenon of data hiding in quantum states.Comment: 35 pages, 6 figures; v2 minor corrections; v3 published versio

Entanglement temperature in molecular magnets composed of S-spin dimers

In the present work, we investigate the quantum thermal entanglement in molecular magnets composed of dimers of spin $S$, using an Entanglement Witness built from measurements of magnetic susceptibility. An entanglement temperature, $T_{e}$, is then obtained for some values of spin $S$. From this, it is shown that $T_{e}$ is proportional to the intradimer exchange interaction $J$ and that entanglement appears only for antiferromagnetic coupling. The results are compared to experiments carried on three isostructural materials: KNaMSi$_{4}$O$_{10}$ (M$=$Mn, Fe or Cu).Comment: accepted for publication in EP

Variabilidade genética em populações de Anticarsia gemmatalis Hübner (Lepidoptera: Noctuidae) nas regiões produtoras de soja no Brasil.

Com o uso de ferramentas moleculares é possível sequenciar genes e caracterizar populações de insetos. Assim, este trabalho teve por objetivo estudar a variabilidade genética entre subpopulações de Anticarsia gemmatalis Hübner (Lepidoptera: Noctuidae) nas principais regiões produtoras de soja, utilizando sequências de genes mitocondriais. Foram coletadas populações de A. gemmatalis nas localidades de: Santa Helena de Goiás (GO), Luis Eduardo Magalhães (BA); Mauá da Serra (PR), Coxilha (RS) e Campo Verde (MT), seu DNA foi extraído para amplificação e sequenciamento. A Análise de Variância Molecular (AMOVA) foi aplicada para estimar a estrutura genética utilizando três fragmentos do mtDNA, o gene da subunidade de citocromo oxidase I (COI), citocromo oxidase II (COII) e citocromo B (CytB). A distribuição e frequência de haplótipos foi determinada pelo programa TCS. Foi sequenciado um total de 71 indivíduos de A. gemmatalis. A subpopulação de MT apresentou a menor variação na frequência dos haplótipos para todas as regiões estudadas. O haplótipo mais representativo foi o h2, sendo encontrado em indivíduos da Bahia (9), Paraná (1) e Rio Grande do Sul (1). A maior frequência haplotípica foi observada em MT, PR e RS. Na análise das sequencias de A. gemmatalis foi possível observar que há potencial para identificar possíveis haplótipos que possam caracterizar uma determinada subpopulação. Para isso seria necessário à utilização de outras ferramentas, como por exemplo, estudos de PCR-RFLP e análise de outras regiões gênicas, que possam contribuir na identificação de haplótipos nas subpopulações de A. gemmatalis no Brasil

Variabilidade genética em populações de Pseudoplusia includens (Walker) (Lepidoptera: Noctuidae) nas regiões produtoras de soja no Brasil.

Pseudoplusia includens (Walker) (Lepidoptera: Noctuidae) é uma importante praga, de difícil controle, na cultura da soja no Brasil. Informações sobre a distribuição da variabilidade de suas subpopulações no Brasil ainda são restritas, embora os conhecimentos da estrutura genética populacional e do fluxo gênico dessa espécie possam contribuir no delineamento do manejo da resistência a inseticidas e toxinas. Assim, este trabalho teve por objetivo estudar a variabilidade genética de P. includens nas principais regiões produtoras de soja, utilizando sequências de genes mitocondriais (mtDNA). Foram coletadas populações de P. includens nas localidades de Campo Verde (MT), Tasso Fragoso (MA), Bela Vista do Paraíso (PR), Santa Helena de Goiás (GO) e Coxilha (RS), totalizando 67 espécimes. O DNA total foi extraído individualmente, e as regiões do mtDNA, citocromo oxidase I (COI), citocromo oxidase II (COII) e citocromo B (CytB) foram amplificadas, purificadas e sequenciadas. A distribuição da variabilidade genética entre e dentro de cada subpopulação foi determinada por meio da Análise de Variância Molecular (AMOVA), usando o programa Arlequin e a frequência de haplótipos foi determinada no programa TCS. As subpopulações dos estados de Goiás e Maranhão foram as que apresentaram a maior diversidade haplotípica. O índice de fixação (ϕST) obtido pela AMOVA indicou que não existe estruturação nas subpopulações estudadas de P. includens. A ausência de agrupamento na análise da rede de haplótipos das sequências de mtDNA evidenciou a reduzida diferenciação entre as subpopulações

Dynamic Collection Scheduling Using Remote Asset Monitoring: Case Study in the UK Charity Sector

Remote sensing technology is now coming onto the market in the waste collection sector. This technology allows waste and recycling receptacles to report their fill levels at regular intervals. This reporting enables collection schedules to be optimized dynamically to meet true servicing needs in a better way and so reduce transport costs and ensure that visits to clients are made in a timely fashion. This paper describes a real-life logistics problem faced by a leading UK charity that services its textile and book donation banks and its high street stores by using a common fleet of vehicles with various carrying capacities. Use of a common fleet gives rise to a vehicle routing problem in which visits to stores are on fixed days of the week with time window constraints and visits to banks (fitted with remote fill-monitoring technology) are made in a timely fashion so that the banks do not become full before collection. A tabu search algorithm was developed to provide vehicle routes for the next day of operation on the basis of the maximization of profit. A longer look-ahead period was not considered because donation rates to banks are highly variable. The algorithm included parameters that specified the minimum fill level (e.g., 50%) required to allow a visit to a bank and a penalty function used to encourage visits to banks that are becoming full. The results showed that the algorithm significantly reduced visits to banks and increased profit by up to 2.4%, with the best performance obtained when the donation rates were more variable