Analytical expression of Genuine Tripartite Quantum Discord for Symmetrical X-states

The study of classical and quantum correlations in bipartite and multipartite systems is crucial for the development of quantum information theory. Among the quantifiers adopted in tripartite systems, the genuine tripartite quantum discord (GTQD), estimating the amount of quantum correlations shared among all the subsystems, plays a key role since it represents the natural extension of quantum discord used in bipartite systems. In this paper, we derive an analytical expression of GTQD for three-qubit systems characterized by a subclass of symmetrical X-states. Our approach has been tested on both GHZ and maximally mixed states reproducing the expected results. Furthermore, we believe that the procedure here developed constitutes a valid guideline to investigate quantum correlations in form of discord in more general multipartite systems.Comment: 13 pages, 4 figures. v3: Added some references and corrected some typo

Time-dependent simulation and analytical modelling of electronic Mach-Zehnder interferometry with edge-states wave packets

We compute the exact single-particle time-resolved dynamics of electronic Mach-Zehnder interferometers based on Landau edge-states transport, and assess the effect of the spatial localization of carriers on the interference pattern. The exact carrier dynamics is obtained by solving numerically the time-dependent Schroedinger equation with a suitable 2D potential profile reproducing the interferometer design. An external magnetic field, driving the system to the quantum Hall regime with filling factor one, is included. The injected carriers are represented by a superposition of edge states and their interference pattern reproduces the results of Y.Ji et al.[Nature 422, 415 (2003)]. By tuning the system towards different regimes, we find two additional features in the transmission spectra, both related to carrier localization, namely a damping of the Aharonov-Bohm oscillations with increasing difference in the arms length, and an increased mean transmission that we trace to the energy-dependent transmittance of quantum point contacts. Finally, we present an analytical model, also accounting for the finite spatial dispersion of the carriers, able to reproduce the above effects.Comment: two-columns, 12 pages, 9 figures; added 10 refs.; main text modified; corrected few typos; added 3 figures of Supplementary Dat

Probing the sign of on-site Hubbard interaction by two-particle quantum walks

We consider two identical bosons propagating on a one-dimensional lattice and address the prob- lem of discriminating whether their mutual on-site interaction is attractive or repulsive. We suggest a probing scheme based on the properties of the corresponding two-particle quantum walks, and show that the sign of the interaction introduces specific and detectable features in the dynamics of quantum correlations, thus permitting to discriminate between the two cases. We also discuss how these features are connected to the band-structure of the Hubbard Hamiltonian, and prove that discrimination may be obtained only when the two walkers are initially prepared in a superposition of localized states.Comment: 9 pages, 9 figure

Time-dependent modelling of single-electron interferometry with edge-states

We simulate the time-resolved dynamics of localized electrons in a 2DEG system, where an external magnetic eld creates quantum Hall edge states, and properly polarized split gates dene a Mach-Zehnder electron interferometer. The carriers travelling inside the Hall channels consist of localized wave packets of edge states: they are propagated numerically by means of a Fourier split-step approach. We find that the energy-dependent scattering process at the quantum point contacts, together with the nite energy distribution of the carriers, have a remarkable eect on the transmission coecient T of the device. We provide an analytical model to justify the characteristics of T which is in good agreement with the numerical simulations

Quantum correlations of identical particles subject to classical environmental noise

Abstract In this work, we propose a measure for the quantum discord of indistinguishable particles, based on the definition of entanglement of particles given in Wiseman and Vaccaro (Phys Rev Lett 91:097902, 2003. doi:10.1103/PhysRevLett.91. 097902). This discord of particles is then used to evaluate the quantum correlations in a system of two identical bosons (fermions), where the particles perform a quantum random walk described by the Hubbard Hamiltonian in a 1D lattice. The dynamics of the particles is either unperturbed or subject to a classical environmental noise—such as random telegraph, pink or brown noise. The observed results are consistent with those for the entanglement of particles, and we observe that on-site interaction between particles have an important protective effect on correlations against the decoherence of the system

Dynamics of copropagating edge states in a multichannel Mach-Zender interferometer

We study numerically a multichannel electronic Mach-Zender interferometer, where an orthogonal magnetic field produces edge states. Our time-dependent model is based on the split-step Fourier method and describes the charge carrier as a Gaussian wavepacket of edge states, whose path is defined by split-gate induced potential profiles on the 2DEG at filling factor 2. We analyse a beam splitter with ∼ 50% inter-channel mixing and obtain Aharonov-Bohm oscillations in the transmission probability of the second channel

Dynamics and Hall-edge-state mixing of localized electrons in a two-channel Mach-Zehnder interferometer

We present a numerical study of a multichannel electronicMach-Zehnder interferometer, based onmagnetically driven noninteracting edge states. The electron path is defined by a full-scale potential landscape on the twodimensional electron gas at filling factor 2, assuming initially only the first Landau level as filled.We tailor the two beamsplitters with 50% interchannelmixing and measure Aharonov-Bohm oscillations in the transmission probability of the second channel.We perform time-dependent simulations by solving the electron Schr\uf6dinger equation through a parallel implementation of the split-step Fourier method, and we describe the charge-carrier wave function as a Gaussian wave packet of edge states.We finally develop a simplified theoretical model to explain the features observed in the transmission probability, and we propose possible strategies to optimize gate performances

Tolerant pearl millet (Pennisetum glaucum (L.) R. Br.) varieties to low soil P have higher transpiration efficiency and lower flowering delay than sensitive ones

Abstract Background and aim In the West African Sahel low soil phosphorus (P) and unpredictable rainfall are major interacting constraints to growth and grain yield of pearl millet. Investigating the relationship between transpiration and final yield under the combined effect of water and P stress is fundamental to understand the underlying mechanisms of tolerance and improve breeding programs. Methods We conducted two lysimeter trials using 1 m long PVC tubes (35 cm diameter) filled with a P poor Sahelian soil mimicking soil profiles to assess grain and stover yield, and water use of 15 pearl millet genotypes grown under different P (no P supply or addition of 1.5 g P tube−1) and water (well watered or terminal water stress) regimes. In experiment 2 transpiration was measured twice a week from tube weight differences, and transpiration efficiency (TE) was calculated as dry matter (DM) produced per kg of water transpired. Results Low soil P delayed flowering, and more so in sensitive genotypes. Later flowering of genotypes sensitive to low P made them more sensitive to terminal water stress. Under P limiting soil, genotypes tolerant and sensitive to low P used similar amounts of water (19.8 and 21.7 kg water plant−1, respectively). However, tolerant lines transpired less water prior to anthesis (8.8 kg water plant−1) leaving more water available for grain filling (11 kg water plant−1) while sensitive lines used 14.4 kg water plant−1 pre-anthesis, leaving only 7.2 kg water plant−1 for grain filling. Low soil P decreased grain yield by affecting seed size at harvest and its damage during seed filling overrode the effect of seed size at sowing. Grain yield was positively correlated with water extracted after anthesis. TE was enhanced by P supply, especially in sensitive lines, and TE was higher in tolerant than in sensitive genotypes under low soil P. Conclusions Pearl millet plants tolerant to low P were more resistant to the delay of flowering caused by low P soil and they presented higher transpiration efficiency. The pattern of transpiration was important to cope with terminal water stress under different levels of P availability. Higher transpiration after anthesis, resulting from conservative water mechanism pre-anthesis (higher TE) and possibly by a shorter delay in flowering under low soil P, enhanced grain yield

Effects of early mycorrhization and colonized root length on low-soil-phosphorus resistance of West African pearl millet

Phosphorus (P) deficiency at early seedling stages is a critical determinant for survival and final yield of pearl millet in multi-stress Sahelian environments. Longer roots and colonization with arbuscular mycorrhizal fungi (AMF) enhance P uptake and crop performance of millet. Assessing the genotypic variation of early mycorrhization and its effect on plant growth is necessary to better understand mechanisms of resistance to low soil P and to use them in breeding strategies for low P. Therefore, in this study, eight pearl millet varieties contrasting in low-P resistance were grown in pots under low P (no additional P supply) and high P (+ 0.4 g P pot−1) conditions, and harvested 2, 4, 6, and 8 weeks after sowing (WAS). Root length was calculated 2 WAS by scanning of dissected roots and evaluation with WinRhizo software. AM infection (%) and P uptake (shoot P concentration multiplied per shoot dry matter) were measured at each harvest. Across harvests under low P (3.3 mg Bray P kg−1), resistant genotypes had greater total root length infected with AMF (837 m), higher percentage of AMF colonization (11.6%), and increased P uptake (69.4 mg P plant−1) than sensitive genotypes (177 m, 7.1% colonization and 46.4 mg P plant−1, respectively). Two WAS, resistant genotypes were infected almost twice as much as sensitive ones (4.1% and 2.1%) and the individual resistant genotypes differed in the percentage of AMF infection. AMF colonization was positively related to final dry matter production in pots, which corresponded to field performance. Early mycorrhization enhanced P uptake in pearl millet grown under P-deficient conditions, with the genotypic variation for this parameter allowing selection for better performance under field conditions

Overcoming phosphorus deficiency in West African pearl millet and sorghum production systems: promising options for crop improvement

West Africa (WA) is among the most food insecure regions. Rapid human population growth and stagnating crop yields greatly contribute to this fact. Poor soil fertility, especially low plant available phosphorus (P) is constraining food production in the region. P-fertilizer use in WA is among the lowest in the world due to inaccessibility and high prices, often unaffordable to resource-poor subsistence farmers. This article provides an overview of soil P-deficiency in WA and opportunities to overcome it by exploiting sorghum and pearl millet genetic diversity. The topic is examined from the perspectives of plant breeding, soil science, plant physiology, plant nutrition, and agronomy, thereby referring to recent results obtained in a joint interdisciplinary research project, and reported literature. Specific objectives are to summarize: (1) The global problem of P scarcity and how it will affect WA farmers; (2) Soil P dynamics in WA soils; (3) Plant responses to P deficiency; (4) Opportunities to breed for improved crop adaptation to P-limited conditions; (5) Challenges and trade-offs for improving sorghum and pearl millet adaptation to low-P conditions in WA; and (6) Systems approaches to address soil P-deficiency in WA. Sorghum and pearl millet in WA exhibit highly significant genetic variation for P-uptake efficiency, P-utilization efficiency, and grain yield under P-limited conditions indicating the possibility of breeding P-efficient varieties. Direct selection under P-limited conditions was more efficient than indirect selection under high-P conditions. Combining P-uptake and P-utilization efficiency is recommendable for WA to avoid further soil mining. Genomic regions responsible for P-uptake, P-utilization efficiency, and grain yield under low-P have been identified in WA sorghum and pearl millet, and marker-assisted selection could be possible once these genomic regions are validated. Developing P-efficient genotypes may not, however, be a sustainable solution in itself in the long-term without replenishing the P removed from the system in harvested produce. We therefore propose the use of integrated soil fertility management and systems-oriented management such as enhanced crop-tree-livestock integration in combination with P-use-efficiency-improved varieties. Recycling P from animal bones, human excreta and urine are also possible approaches toward a partially closed and efficient P cycle in WA