The Ante-Nicene fathers : translations of the writings of the fathers down to A.D. 325 /

First published under title: Ante-Nicene Christian library, Edinburgh, 1867-97.

Bitwise bell-inequality violations for an entangled state involving 2N ions

Following on from previous work [J.-A. Larsson, Phys. Rev. A 67, 022108 (2003)], Bell inequalities based on correlations between binary digits are considered for a particular entangled state involving 2N trapped ions. These inequalities involve applying displacement operations to half of the ions and then measuring correlations between pairs of corresponding bits in the binary representations of the number of center-of-mass phonons of N particular ions. It is shown that the state violates the inequalities and thus displays nonclassical correlations. It is also demonstrated that it violates a Bell inequality when the displacements are replaced by squeezing operations.

Transmission of optical coherent-state qubits

We discuss the long-distance transmission of qubits encoded in optical coherent states. Through absorption, these qubits suffer from two main types of errors, namely the reduction of the amplitude of the coherent states and accidental application of the Pauli Z operator. We show how these errors can be fixed using techniques of teleportation and error-correcting codes.

Demonstrating superior discrimination of locally prepared states using nonlocal measurements

We experimentally demonstrate the superior discrimination of separated, unentangled two-qubit correlated states using nonlocal measurements, when compared with measurements based on local operations and classical communications. When predicted theoretically, this phenomenon was dubbed quantum nonlocality without entanglement. We characterize the performance of the nonlocal, or joint, measurement with a payoff function, for which we measure 0.72 +/- 0.02, compared with the maximum locally achievable value of 2/3 and the overall optimal value of 0.75.

Simulating Hamiltonian dynamics using many-qudit Hamiltonians and local unitary control

When can a quantum system of finite dimension be used to simulate another quantum system of finite dimension? What restricts the capacity of one system to simulate another? In this paper we complete the program of studying what simulations can be done with entangling many-qudit Hamiltonians and local unitary control. By entangling we mean that every qudit is coupled to every other qudit, at least indirectly. We demonstrate that the only class of finite-dimensional entangling Hamiltonians that are not universal for simulation is the class of entangling Hamiltonians on qubits whose Pauli operator expansion contains only terms coupling an odd number of systems, as identified by Bremner [Phys. Rev. A 69, 012313 (2004)]. We show that in all other cases entangling many-qudit Hamiltonians are universal for simulation.

A geometric approach to quantum circuit lower bounds

What is the minimal size quantum circuit required to exactly implement a specified n-qubit unitary operation, U, without the use of ancilla qubits? We show that a lower bound on the minimal size is provided by the length of the minimal geodesic between U and the identity, I, where length is defined by a suitable Finsler metric on the manifold SU(2(n)). The geodesic curves on these manifolds have the striking property that once an initial position and velocity are set, the remainder of the geodesic is completely determined by a second order differential equation known as the geodesic equation. This is in contrast with the usual case in circuit design, either classical or quantum, where being given part of an optimal circuit does not obviously assist in the design of the rest of the circuit. Geodesic analysis thus offers a potentially powerful approach to the problem of proving quantum circuit lower bounds. In this paper we construct several Finsler metrics whose minimal length geodesics provide lower bounds on quantum circuit size. For each Finsler metric we give a procedure to compute the corresponding geodesic equation. We also construct a large class of solutions to the geodesic equation, which we call Pauli geodesics, since they arise from isometries generated by the Pauli group. For any unitary U diagonal in the computational basis, we show that: (a) provided the minimal length geodesic is unique, it must be a Pauli geodesic; (b) finding the length of the minimal Pauli geodesic passing from I to U is equivalent to solving an exponential size instance of the closest vector in a lattice problem (CVP); and (c) all but a doubly exponentially small fraction of such unitaries have minimal Pauli geodesics of exponential length.

Entanglement under restricted operations: Analogy to mixed-state entanglement

We show that the classification of bipartite pure entangled states when local quantum operations are restricted yields a structure that is analogous in many respects to that of mixed-state entanglement. Specifically, we develop this analogy by restricting operations through local superselection rules, and show that such exotic phenomena as bound entanglement and activation arise using pure states in this setting. This analogy aids in resolving several conceptual puzzles in the study of entanglement under restricted operations. In particular, we demonstrate that several types of quantum optical states that possess confusing entanglement properties are analogous to bound entangled states. Also, the classification of pure-state entanglement under restricted operations can be much simpler than for mixed-state entanglement. For instance, in the case of local Abelian superselection rules all questions concerning distillability can be resolved.

Greenberger-Horne-Zeilinger-type and W-type entangled coherent states: Generation and Bell-type inequality tests without photon counting

We study Greenberger-Horne-Zeilinger-type (GHZ-type) and W-type three-mode entangled coherent states. Both types of entangled coherent states violate Mermin's version of the Bell inequality with threshold photon detection (i.e., without photon counting). Such an experiment can be performed using linear optics elements and threshold detectors with significant Bell violations for GHZ-type entangled coherent states. However, to demonstrate Bell-type inequality violations for W-type entangled coherent states, additional nonlinear interactions are needed. We also propose an optical scheme to generate W-type entangled coherent states in free-traveling optical fields. The required resources for the generation are a single-photon source, a coherent state source, beam splitters, phase shifters, photodetectors, and Kerr nonlinearities. Our scheme does not necessarily require strong Kerr nonlinear interactions; i.e., weak nonlinearities can be used for the generation of the W-type entangled coherent states. Furthermore, it is also robust against inefficiencies of the single-photon source and the photon detectors.

Better Bell-inequality violation by collective measurements

The standard Bell-inequality experiments test for violation of local realism by repeatedly making local measurements on individual copies of an entangled quantum state. Here we investigate the possibility of increasing the violation of a Bell inequality by making collective measurements. We show that the nonlocality of bipartite pure entangled states, quantified by their maximal violation of the Bell-Clauser-Horne inequality, can always be enhanced by collective measurements, even without communication between the parties. For mixed states we also show that collective measurements can increase the violation of Bell inequalities, although numerical evidence suggests that the phenomenon is not common as it is for pure states.

The 'hard problem' and the quantum physicists. Part 1:the first generation

All four of the most important figures in the early twentieth-century development of quantum physics-Niels Bohr, Erwin Schroedinger, Werner Heisenberg and Wolfgang Pauli-had strong interests in the traditional mind-brain, or 'hard,' problem. This paper reviews their approach to this problem, showing the influence of Bohr's complementarity thesis, the significance of Schroedinger's small book, 'What is life?,' the updated Platonism of Heisenberg and, perhaps most interesting of all, the interaction of Carl Jung and Wolfgang Pauli in the latter's search for a unification of mind and matter. © 2005 Elsevier Inc. All rights reserved.

Exact solution of the Bragg-diffraction problem in sillenites

A method for the exact solution of the Bragg-difrraction problem for a photorefractive grating in sillenite crystals based on Pauli matrices is proposed. For the two main optical configurations explicit analytical expressions are found for the diffraction efficiency and the polarization of the scattered wave. The exact solution is applied to a detailed analysis of a number of particular cases. For the known limiting cases there is agreement with the published results.

Exact solution of the Bragg-diffraction problem in sillenites

A method for the exact solution of the Bragg-difrraction problem for a photorefractive grating in sillenite crystals based on Pauli matrices is proposed. For the two main optical configurations explicit analytical expressions are found for the diffraction efficiency and the polarization of the scattered wave. The exact solution is applied to a detailed analysis of a number of particular cases. For the known limiting cases there is agreement with the published results.

Evaluation of TerraSAR-X Observations for Wetland InSAR Application

This paper assesses the potential of using spaceborne X-band synthetic aperture radar (SAR) data for monitoring water-level changes over wetlands. Our analysis is based on three sets of TerraSAR-X (TSX) observations acquired over South Florida's Everglades wetlands during an eight-month period in 2008. The first set was acquired in single HH polarization stripmap mode over our northern study area, consisting of managed wetlands and urban environments. The second set was acquired in dual-polarization stripmap mode over the western half of the same area, consisting mostly of managed wetlands. The third set was also acquired with dual-polarization stripmap mode over our southern study area, consisting of natural flow freshand salt-water wetlands in the southern Everglades. The first data set was used for a proof-of-concept study to verify that X-band data can generate coherent interferograms in wetland areas. Interferometric processing of this data set shows a high level of coherence (> 0.35) over both wetland and urban regions, maintaining interferometric phase in all three interferograms spanning 11 days. Surprisingly, phase is maintained over some of the wetlands even for interferograms spanning 33 days. The other two data sets were used to evaluate interferometric coherence of all four polarization modes and to determine dominant scattering mechanism in each wetland environment. Our results show high coherence values (> 0.4) in all polarization modes, with highest values in HH, then VV, and lowest in HV or VH. Interferograms calculated from multipolarization data show very similar fringe patterns regardless of the polarization type, suggesting that the phase information in all polarization data reflects water-level changes in wetlands and that volume scattering may be less important than commonly believed. We also used the two multipolarization data sets to conduct the Pauli decomposition, finding a strong dependence of scattering mechanism on vegetation t- - ype. The high interferometric coherence level of all polarization data suggests that a significant part of the X-band scattered signal interacts with lower sections of the vegetation (trunks and branches), because scattering from wind-affected canopies cannot support such a high coherence level. The high spatial resolution of TSX, combined with its 11-day repeat orbit, makes this X-band sensor surprisingly suitable for wetland interferometric SAR applications.

Benchmarking a modified version of the civ3 nonrelativistic atomic-structure code within Na-like-tungsten R -matrix calculations

In this work we explore the validity of employing a modified version of the nonrelativistic structure code civ3 for heavy, highly charged systems, using Na-like tungsten as a simple benchmark. Consequently, we present radiative and subsequent collisional atomic data compared with corresponding results from a fully relativistic structure and collisional model. Our motivation for this line of study is to benchmark civ3 against the relativistic grasp0 structure code. This is an important study as civ3 wave functions in nonrelativistic R-matrix calculations are computationally less expensive than their Dirac counterparts. There are very few existing data for the W LXIV ion in the literature with which we can compare except for an incomplete set of energy levels available from the NIST database. The overall accuracy of the present results is thus determined by the comparison between the civ3 and grasp0 structure codes alongside collisional atomic data computed by the R-matrix Breit-Pauli and Dirac codes. It is found that the electron-impact collision strengths and effective collision strengths computed by these differing methods are in good general agreement for the majority of the transitions considered, across a broad range of electron temperatures.

Farmers’ knowledge and use of soil fauna in agriculture: a worldwide review

General knowledge of the small, invisible, or hidden organisms that make soil one of the most biodiverse habitats on Earth is thought to be scarce, despite their importance in food systems and agricultural production. We provide the first worldwide review of high-quality research that reports on farmers’ knowledge of soil organisms in agriculture. The depth of farmers’ knowledge varied; some farming communities held detailed local taxonomies and observations of soil biota, or used soil biological activity as indicators of soil fertility, while others were largely unaware of soil fauna. Elicitation of soil biota knowledge was often incidental to the main research goal in many of the reviewed studies. Farmers are rarely deliberately or deeply consulted by researchers on their existing knowledge of soil biota, soil ecology, or soil ecological processes. Deeper understanding of how farmers use and value soil life can lead to more effective development of collaborative extension programs, policies, and management initiatives directed at maintaining healthy, living soils.