ABSTRACT
At the limit of an infinite confinement strength ω, the ground state of a system that comprises two fermions or bosons in harmonic confinement interacting through the Fermi-Huang pseudopotential remains strongly correlated. A detailed analysis of the one-particle description of this "contactium" reveals several peculiarities that are not encountered in conventional model systems (such as the two-electron harmonium atom, ballium, and spherium) involving Coulombic interparticle interactions. First of all, none of the natural orbitals (NOs) {ψn(ω;r)} of the contactium is unoccupied, which implies nonzero collective occupancies for all the angular momenta. Second, the NOs and their non-ascendingly ordered occupation numbers {νn} turn out to be related to the eigenfunctions and eigenvalues of a zero-energy Schrödinger equation with an attractive Gaussian potential. This observation enables the derivation of their properties, such as the n-4/3 asymptotic decay of νn at the nâ∞ limit (which differs from that of n-8/3 in the Coulombic systems), the independence of the confinement energy vn=⟨ψn(ω;r)|12ω2r2|ψn(ω;r)⟩ of n, and the n-2/3 asymptotic decay of the respective contribution νntn to the kinetic energy. Upon suitable scaling, the weakly occupied NOs of the contactium turn out to be virtually identical to those of the two-electron harmonium atom at the ω â ∞ limit, despite the entirely different interparticle interactions in these systems.
ABSTRACT
Biogeochemical redox processes control the chemical behavior of many major and trace elements, making their comprehension crucial for predicting and protecting environmental health. Nitrogen (N) is especially susceptible to changes in soil redox conditions and affects the cycles of other redox-sensitive species. Elevated N concentrations, in nitrate form, in agricultural soils and associated freshwater ecosystems constitute a problem in many parts of the world. Although a wide variety of measures have been adopted, their assessment through concentration measurements in groundwater and surface water of the different monitoring networks has shortcomings. Nitrate, as a non-point pollutant, is subject to several processes (e.g., transformation and retardation) before it is detected, making it impossible to evaluate measurements' effectiveness reliably. Thus, we designed and constructed a monitoring station featuring commercially available products and self-manufactured components at an agricultural site for the in situ assessment of nitrate-related processes by high-resolution monitoring of hydraulic (soil water content, matric potential, groundwater head) and hydrogeochemical variables (oxidation-reduction potential and groundwater and pore water chemistry) within the vadose zone and the shallow aquifer. The monitoring station has proven to be a reliable tool. Changes over depth and time of measured variables have been identified, allowing the detection of the transient behavior of the redox reactive zone and the interpretation of ongoing denitrification processes and other redox nitrate-triggered phenomena, such as uranium roll-front and selenium accumulation at the redox interface. Measuring both geochemical and soil water variables allows for the calculation of in situ solute inputs into the groundwater and their reaction rates.
Subject(s)
Groundwater , Water Pollutants, Chemical , Nitrates/analysis , Ecosystem , Environmental Monitoring , Water Pollutants, Chemical/analysis , Groundwater/chemistry , Soil , Water , Oxidation-ReductionABSTRACT
Multinomial models can be difficult to use when constraints are placed on the probabilities. An exact model checking procedure for such models is developed based on a uniform prior on the full multinomial model. For inference, a nonuniform prior can be used and a consistency theorem is proved concerning a check for prior-data conflict with the chosen prior. Applications are presented and a new elicitation methodology is developed for multinomial models with ordered probabilities.
ABSTRACT
We report an experiment in which one determines, with least tomographic effort, whether an unknown two-photon polarization state is entangled or separable. The method measures whole families of optimal entanglement witnesses. We introduce adaptive measurement schemes that greatly speed up the entanglement detection. The experiments are performed on states of different ranks, and we find good agreement with results from computer simulations.
ABSTRACT
Quantum-state reconstruction on a finite number of copies of a quantum system with informationally incomplete measurements, as a rule, does not yield a unique result. We derive a reconstruction scheme where both the likelihood and the von Neumann entropy functionals are maximized in order to systematically select the most-likely estimator with the largest entropy, that is, the least-bias estimator, consistent with a given set of measurement data. This is equivalent to the joint consideration of our partial knowledge and ignorance about the ensemble to reconstruct its identity. An interesting structure of such estimators will also be explored.
ABSTRACT
The security of a cryptographic key that is generated by communication through a noisy quantum channel relies on the ability to distill a shorter secure key sequence from a longer insecure one. For an important class of protocols, which exploit tomographically complete measurements on entangled pairs of any dimension, we show that the noise threshold for classical advantage distillation is identical with the threshold for quantum entanglement distillation. As a consequence, the two distillation procedures are equivalent: neither offers a security advantage over the other.
ABSTRACT
We propose entropic measures for the strength of single-particle and two-particle interference in interferometric experiments where each particle of a pair traverses a multipath interferometer. Optimal single-particle interference excludes any two-particle interference, and vice versa. We report an inequality that states the compromises allowed by quantum mechanics in intermediate situations, and identify a class of two-particle states for which the upper bound is reached. Our approach is applicable to symmetric two-partite systems of any finite dimension.
ABSTRACT
In the 1987 spin-retrodiction puzzle of Vaidman, Aharonov, and Albert one is challenged to ascertain the values of sigma(x), sigma(y), and sigma(z) of a spin-1/2 particle by utilizing entanglement. We report the experimental realization of a quantum-optical version in which the outcome of an intermediate polarization projection is inferred by exploiting single-photon two-qubit quantum gates. The experimental success probability is consistently above the 90.2% threshold of the optimal one-qubit strategy, with an average success probability of 95.6%.