To freeze or not to: Quantum correlations under local decoherence

We provide necessary and sufficient conditions for freezing of quantum correlations as measured by quantum discord and quantum work deficit in the case of bipartite as well as multipartite states subjected to local noisy channels. We recognize that inhomogeneity of the magnetizations of the shared quantum states plays an important role in the freezing phenomena. We show that the frozen value of the quantum correlation and the time interval for freezing follow a complementarity relation. For states which do not exhibit "exact" freezing, but can be frozen "effectively", by having a very slow decay rate with suitable tuning of the state parameters, we introduce an index -- the freezing index -- to quantify the goodness of freezing. We find that the freezing index can be used to detect quantum phase transitions and discuss the corresponding scaling behavior.Comment: 14 pages, 9 figures, close to published version, title changed by Phys. Rev. A. to 'Freezing of quantum correlations under local decoherence

Static and dynamical quantum correlations in phases of an alternating field XY model

We investigate the static and dynamical patterns of entanglement in an anisotropic XY model with an alternating transverse magnetic field, which is equivalent to a two-component one-dimensional Fermi gas on a lattice, a system realizable with current technology. Apart from the antiferromagnetic and paramagnetic phases, the model possesses a dimer phase which is not present in the transverse XY model. At zero temperature, we find that the first derivative of bipartite entanglement can detect all the three phases. We analytically show that the model has a "factorization line" on the plane of system parameters, in which the zero temperature state is separable. Along with investigating the effect of temperature on entanglement in a phase plane, we also report a non-monotonic behavior of entanglement with respect to temperature in the anti-ferromagnetic and paramagnetic phases, which is surprisingly absent in the dimer phase. Since the time dynamics of entanglement in a realizable physical system plays an important role in quantum information processing tasks, the evolutions of entanglement at small as well as large time are examined. Consideration of large time behavior of entanglement helps us to prove that in this model, entanglement is always ergodic. We observe that other quantum correlation measures can qualitatively show similar features in zero and finite temperatures. However, unlike nearest-neighbor entanglement, the nearest-neighbor information theoretic measures can be both ergodic as well as non-ergodic, depending on the system parameters.Comment: 20 Pages, 13 Figures, 2 Tables, Published versio

Reducing Computational Complexity of Quantum Correlations

We address the issue of reducing the resource required to compute information-theoretic quantum correlation measures like quantum discord and quantum work deficit in two qubits and higher dimensional systems. We show that determination of the quantum correlation measure is possible even if we utilize a restricted set of local measurements. We find that the determination allows us to obtain a closed form of quantum discord and quantum work deficit for several classes of states, with a low error. We show that the computational error caused by the constraint over the complete set of local measurements reduces fast with an increase in the size of the restricted set, implying usefulness of constrained optimization, especially with the increase of dimensions. We perform quantitative analysis to investigate how the error scales with the system size, taking into account a set of plausible constructions of the constrained set. Carrying out a comparative study, we show that the resource required to optimize quantum work deficit is usually higher than that required for quantum discord. We also demonstrate that minimization of quantum discord and quantum work deficit is easier in the case of two-qubit mixed states of fixed ranks and with positive partial transpose in comparison to the corresponding states having non-positive partial transpose. Applying the methodology to quantum spin models, we show that the constrained optimization can be used with advantage in analyzing such systems in quantum information-theoretic language. For bound entangled states, we show that the error is significantly low when the measurements correspond to the spin observables along the three Cartesian coordinates, and thereby we obtain expressions of quantum discord and quantum work deficit for these bound entangled states.Comment: 19 pages, 14 figures, 3 table

Insecticide resistance and the future of malaria control in Zambia.

BACKGROUND: In line with the Global trend to improve malaria control efforts a major campaign of insecticide treated net distribution was initiated in 1999 and indoor residual spraying with DDT or pyrethroids was reintroduced in 2000 in Zambia. In 2006, these efforts were strengthened by the President's Malaria Initiative. This manuscript reports on the monitoring and evaluation of these activities and the potential impact of emerging insecticide resistance on disease transmission. METHODS: Mosquitoes were captured daily through a series of 108 window exit traps located at 18 sentinel sites. Specimens were identified to species and analyzed for sporozoites. Adult Anopheles mosquitoes were collected resting indoors and larva collected in breeding sites were reared to F1 and F0 generations in the lab and tested for insecticide resistance following the standard WHO susceptibility assay protocol. Annual cross sectional household parasite surveys were carried out to monitor the impact of the control programme on prevalence of Plasmodium falciparum in children aged 1 to 14 years. RESULTS: A total of 619 Anopheles gambiae s.l. and 228 Anopheles funestus s.l. were captured from window exit traps throughout the period, of which 203 were An. gambiae malaria vectors and 14 An. funestus s.s.. In 2010 resistance to DDT and the pyrethroids deltamethrin, lambda-cyhalothrin and permethrin was detected in both An. gambiae s.s. and An. funestus s.s.. No sporozoites were detected in either species. Prevalence of P. falciparum in the sentinel sites remained below 10% throughout the study period. CONCLUSION: Both An. gambiae s.s. and An. funestus s.s. were controlled effectively with the ITN and IRS programme in Zambia, maintaining a reduced disease transmission and burden. However, the discovery of DDT and pyrethroid resistance in the country threatens the sustainability of the vector control programme

Statistics of leading digits leads to unification of quantum correlations

We show that the frequency distribution of the first significant digits of the numbers in the data sets generated from a large class of measures of quantum correlations, which are either entanglement measures, or belong to the information-theoretic paradigm, exhibit a universal behaviour. In particular, for Haar uniformly simulated arbitrary two-qubit states, we find that the first-digit distribution corresponding to a collection of chosen computable quantum correlation quantifiers tend to follow the first-digit law, known as the Benford's law, when the rank of the states increases. Considering a two-qubit state which is obtained from a system governed by paradigmatic spin Hamiltonians, namely, the XY model in a transverse field, and the XXZ model, we show that entanglement as well as information theoretic measures violate the Benford's law. We quantitatively discuss the violation of the Benford's law by using a violation parameter, and demonstrate that the violation parameter can signal quantum phase transitions occurring in these models. We also comment on the universality of the statistics of first significant digits corresponding to appropriate measures of quantum correlations in the case of multipartite systems as well as systems in higher dimensions.Comment: v1: 11 pages, 5 figures, 2 tables; v2: 11 pages, 6 figures, 2 tables, new results added, extended version of the published pape