Comment on "Far-field microscopy with a nanometer-scale resolution based on the in-plane image magnification by surface plasmon polaritons"

This is a small comment concerning the work by Smolyaninov et al. in Phys. Rev. Lett.94, 057401 (2005)

On the local unitary equivalence of states of multi-partite systems

Two pure states of a multi-partite system are alway are related by a unitary transformation acting on the Hilbert space of the whole system. This transformation involves multi-partite transformations. On the other hand some quantum information protocols such as the quantum teleportation and quantum dense coding are based on equivalence of some classes of states of bi-partite systems under the action of local (one-particle) unitary operations. In this paper we address the question: ``Under what conditions are the two states states, $\varrho$ and $\sigma$, of a multi-partite system locally unitary equivalent?'' We present a set of conditions which have to be satisfied in order that the two states are locally unitary equivalent. In addition, we study whether it is possible to prepare a state of a multi-qudit system. which is divided into two parts A and B, by unitary operations acting only on the systems A and B, separately.Comment: 6 revtex pages, 1 figur

Quantum Zeno tomography

We show that the resolution "per absorbed particle" of standard absorption tomography can be outperformed by a simple interferometric setup, provided that the different levels of "gray" in the sample are not uniformly distributed. The technique hinges upon the quantum Zeno effect and has been tested in numerical simulations. The scheme we propose could be implemented in experiments with UV-light, neutrons or X-rays.Comment: 8 pages, 5 figure

Experimental GHZ Entanglement beyond Qubits

The Greenberger-Horne-Zeilinger (GHZ) argument provides an all-or-nothing contradiction between quantum mechanics and local-realistic theories. In its original formulation, GHZ investigated three and four particles entangled in two dimensions only. Very recently, higher dimensional contradictions especially in three dimensions and three particles have been discovered but it has remained unclear how to produce such states. In this article we experimentally show how to generate a three-dimensional GHZ state from two-photon orbital-angular-momentum entanglement. The first suggestion for a setup which generates three-dimensional GHZ entanglement from these entangled pairs came from using the computer algorithm Melvin. The procedure employs novel concepts significantly beyond the qubit case. Our experiment opens up the possibility of a truly high-dimensional test of the GHZ-contradiction which, interestingly, employs non-Hermitian operators.Comment: 6+6 pages, 8 figure

Quantum orbital angular momentum of elliptically-symmetric light

We present a quantum mechanical analysis of the orbital angular momentum of a class of recently discovered elliptically-symmetric stable light fields --- the so-called Ince-Gauss modes. We study, in a fully quantum formalism, how the orbital angular momentum of these beams varies with their ellipticity and discover several compelling features, including: non-monotonic behavior, stable beams with real continuous (non-integer) orbital angular momenta, and orthogonal modes with the same orbital angular momenta. We explore, and explain in detail, the reasons for this behavior. These features may have application to quantum key distribution, atom trapping, and quantum informatics in general --- as the ellipticity opens up a new way of navigating the photonic Hilbert space.Comment: 9 Pages, 4 Figures, Comments Welcom

Pollen Processing Behavior of Heliconius Butterflies: A Derived Grooming Behavior

Pollen feeding behaviors Heliconius and Laparus (Lepidoptera: Nymphalidae) represent a key innovation that has shaped other life history traits of these neotropical butterflies. Although all flower visiting Lepidoptera regularly come in contact with pollen, only Heliconius and Laparus butterflies actively collect pollen with the proboscis and subsequently take up nutrients from the pollen grains. This study focused on the behavior of pollen processing and compared the movement patterns with proboscis grooming behavior in various nymphalid butterflies using video analysis. The proboscis movements of pollen processing behavior consisted of a lengthy series of repeated coiling and uncoiling movements in a loosely coiled proboscis position combined with up and down movements and the release of saliva. The proboscis-grooming behavior was triggered by contamination of the proboscis in both pollen feeding and non-pollen feeding nymphalid butterflies. Proboscis grooming movements included interrupted series of coiling and uncoiling movements, characteristic sideways movements, proboscis lifting, and occasionally full extension of the proboscis. Discharge of saliva was more pronounced in pollen feeding species than in non-pollen feeding butterfly species. We conclude that the pollen processing behavior of Heliconius and Laparus is a modified proboscis grooming behavior that originally served to clean the proboscis after contamination with particles

The End of the Great Depression 1939-41: Policy Contributions and Fiscal Multipliers

This paper is about the size of fiscal multipliers and the sources of recovery from the Great Depression. Its baseline result is that 89.1 percent of the 1939:Q1-1941:Q4 recovery can be attributed to fiscal policy innovations, 34.1 percent to monetary policy innovations and the remaining -23.2 percent to the combined effect of the basic VAR dynamic forecast and innovations in non-government components of GDP. Traditional Keynesian multipliers assume that there are no capacity constraints to impede a fiscal-driven expansion in aggregate demand. On the contrary, we find ample evidence of capacity constraints in 1941, particularly in the second half of that year. As a result our preferred government spending multiplier is 1.80 when the time period ends in 1941:Q2 but only 0.88 when the time period ends in supply-constrained 1941:Q4. Only the 1.80 multiplier is relevant to situations like 2009-10 when capacity constraints are absent across the economy. Two sets of new insights emerge from a review of contemporary print media. We document that the American economy went to war starting in June 1940, fully 18 months before Pearl Harbor. We also detail the bifurcated nature of the 1941 economy, with excess capacity in its labor market but capacity constraints in many of the key manufacturing industries. By July 1941, the American economy was in a state of perceived national emergency.

Arbitrary d-dimensional Pauli X gates of a flying qudit

High-dimensional degrees of freedom of photons can encode more quantum information than their two-dimensional counterparts. While the increased information capacity has advantages in quantum applications (such as quantum communication), controlling and manipulating these systems has been challenging. Here we show a method to perform deterministic arbitrary high-dimensional Pauli X gates for single photons carrying orbital angular momentum. The X gate consists of a cyclic permutation of qudit basis vectors and, together with the Z gate, forms the basis for performing arbitrary transformations. The proposed experimental setups only use two basic optical elements such as mode sorters and mode shifters and thus could be implemented in any system where these experimental tools are available. Furthermore the number of involved interferometers scales logarithmically with the dimension, which is important for practical implementation