Generalized Samuel Multiplicities of Monomial Ideals and Volumes

We describe conjecturally the generalized Samuel multiplicities c_0,...,c_{d-1} of a monomial ideal I subset K[x_1,...,x_d] in terms of its Newton polyhedron NP(I). More precisely, we conjecture that c_i equals the sum of the normalized (d-1)-volumes of pyramids over the projections of the (d-i-1)-dimensional compact faces of NP(I) along the infinite-directions of i-unbounded facets in which they are contained. For c_0 proofs are known (Guibert, Jeffries and Monta\uf1o) and for c_{d-1} a proof is given

Efficient measurement-based quantum computing with continuous-variable systems

We present strictly efficient schemes for scalable measurement-based quantum computing using continuous-variable systems: These schemes are based on suitable non-Gaussian resource states, ones that can be prepared using interactions of light with matter systems or even purely optically. Merely Gaussian measurements such as optical homodyning as well as photon counting measurements are required, on individual sites. These schemes overcome limitations posed by Gaussian cluster states, which are known not to be universal for quantum computations of unbounded length, unless one is willing to scale the degree of squeezing with the total system size. We establish a framework derived from tensor networks and matrix product states with infinite physical dimension and finite auxiliary dimension general enough to provide a framework for such schemes. Since in the discussed schemes the logical encoding is finite-dimensional, tools of error correction are applicable. We also identify some further limitations for any continuous-variable computing scheme from which one can argue that no substantially easier ways of continuous-variable measurement-based computing than the presented one can exist.Comment: 13 pages, 3 figures, published versio

Noise-free high-efficiency photon-number-resolving detectors

High-efficiency optical detectors that can determine the number of photons in a pulse of monochromatic light have applications in a variety of physics studies, including post-selection-based entanglement protocols for linear optics quantum computing and experiments that simultaneously close the detection and communication loopholes of Bell's inequalities. Here we report on our demonstration of fiber-coupled, noise-free, photon-number-resolving transition-edge sensors with 88% efficiency at 1550 nm. The efficiency of these sensors could be made even higher at any wavelength in the visible and near-infrared spectrum without resulting in a higher dark-count rate or degraded photon-number resolution.Comment: 4 pages, 4 figures Published in Physical Review A, Rapid Communications, 17 June 200

Experimentally realizable quantum comparison of coherent states and its applications

When comparing quantum states to each other, it is possible to obtain an unambiguous answer, indicating that the states are definitely different, already after a single measurement. In this paper we investigate comparison of coherent states, which is the simplest example of quantum state comparison for continuous variables. The method we present has a high success probability, and is experimentally feasible to realize as the only required components are beam splitters and photon detectors. An easily realizable method for quantum state comparison could be important for real applications. As examples of such applications we present a "lock and key" scheme and a simple scheme for quantum public key distribution.Comment: 14 pages, 5 figures, version one submitted to PRA. Version two is the final accepted versio

Fast quantum key distribution with decoy number states

We investigate the use of photon number states to identify eavesdropping attacks on quantum key distribution (QKD) schemes. The technique is based on the fact that different photon numbers traverse a channel with different transmittivity. We then describe two QKD schemes that utilize this method, one of which overcomes the upper limit on the key generation rate imposed by the dead time of detectors when using a heralded source of photons.Comment: 15 pages, 6 figures; Accepted to J. Mod. Op

Effects of Kapton Sample Cell Windows on the Detection Limit of Smectite: Implications for CheMin on the Mars Science Laboratory Mission

The CheMin instrument on the Mars Science Laboratory (MSL) rover Curiosity is an X-ray diffraction (XRD) and X-ray fluorescence (XRF) instrument capable of providing the mineralogical and chemical compositions of rocks and soils on the surface of Mars. CheMin uses a microfocus X-ray tube with a Co target, transmission geometry, and an energy-discriminating X-ray sensitive CCD to produce simultaneous 2-D XRD patterns and energy-dispersive X-ray histograms from powdered samples. CheMin has two different window materials used for sample cells -- Mylar and Kapton. Instrument details are provided elsewhere. Fe/Mg-smectite (e.g., nontronite) has been identified in Gale Crater, the MSL future landing site, by CRISM spectra. While large quantities of phyllosilicate minerals will be easily detected by CheMin, it is important to establish detection limits of such phases to understand capabilities and limitations of the instrument. A previous study indicated that the (001) peak of smectite at 15 Ang was detectable in a mixture of 1 wt.% smectite with olivine when Mylar is the window material for the sample cell. Complications arise when Kapton is the window material because Kapton itself also has a diffraction peak near 15 Ang (6.8 deg 2 Theta). This study presents results of mineral mixtures of smectite and olivine to determine smectite detection limits for Kapton sample cells. Because the intensity and position of the smectite (001) peak depends on the hydration state, we also analyzed mixtures with "hydrated" and "dehydrated"h smectite to examine the effects of hydration state on detection limits

Investigations Using Laboratory Testbeds to Interpret Flight Instrument Datasets from Mars Robotic Missions

The Astromaterials Research and Exploration Science Directorate at the NASA Johnson Space Center (JSC) has laboratory instrumentation that mimic the capabilities of corresponding flight instruments to enable interpretation of datasets returned from Mars robotic missions. The lab instruments have been and continue to be applied to datasets for the Moessbauer Spectrometer (MB) on the Mars Exploration Rovers (MER), the Thermal & Evolved Gas Analyzer (TEGA) on the Mars Phoenix Scout, the CRISM instrument on the Mars Reconnaissance Orbiter Missions and will be applied to datasets for the Sample Analysis at Mars (SAM), Chemistry and Mineralogy (CheMin) and Chemistry & Camera (ChemCam) instruments onboard the Mars Science Laboratory (MSL). The laboratory instruments can analyze analog samples at costs that are substantially lower than engineering models of flight instruments, but their success to enable interpretation of flight data depends on how closely their capabilities mimic those of the flight instrument. The JSC lab MB instruments are equivalent to the MER instruments except without flight qualified components and no reference channel Co-57 source. Data from analog samples were critical for identification of Mg-Fe carbonate at Gusev crater. Fiber-optic VNIR spectrometers are used to obtain CRISM-like spectral data over the range 350-2500 nm, and data for Fephyllosilicates show irreversible behavior in the electronic transition region upon dessication. The MB and VNIR instruments can be operated within chambers where, for example, the absolute H2O concentration can be measured and controlled. Phoenix's TEGA consisted of a calorimeter coupled to a mass spectrometer (MS). The JSC laboratory testbed instrument consisted of a differential scanning calorimeter (DSC) coupled to a MS configured to operate under total pressure (12 mbar), heating rate (20 C/min), and purge gas composition (N2) analogous to the flight TEGA. TEGA detected CO2 release at both low (400-680 C) and high (725-820 C) temperature and an endothermic reaction in concert with the high temperature release. The high-temperature thermal decomposition is consistent with calcite, dolomite, or ankerite, (3-6 wt.%) or any combination of these phase based upon laboratory testbed experiments. Recent laboratory experiments suggest that the low temperature CO2 release was caused by a reaction between calcium carbonate and hydrated magnesium perchlorate; although, CO2 release by the oxidation of organic materials and Fe-/Mg-rich carbonates cannot be ruled out. MSL landed in Gale crater on August 5, 2012. Although numerous analog samples have been analyzed on the JSC laboratory testbeds, no SAM, CheMin, or ChemCam analyses have been acquired by MSL to date. The JSC SAM laboratory testbed consists of a thermal analyzer coupled with a MS configured to operate under total pressure (30 mbar), heating rate (35 C/min), and purge gas composition (He) analogous to the flight SAM. The CheMin and ChemCam laboratory testbeds were developed and built by inXitu, Inc. and Los Alamos National Laboratory, respectively, to acquire datasets relevant to the MSL CheMin and ChemCam flight instruments

From Linear Optical Quantum Computing to Heisenberg-Limited Interferometry

The working principles of linear optical quantum computing are based on photodetection, namely, projective measurements. The use of photodetection can provide efficient nonlinear interactions between photons at the single-photon level, which is technically problematic otherwise. We report an application of such a technique to prepare quantum correlations as an important resource for Heisenberg-limited optical interferometry, where the sensitivity of phase measurements can be improved beyond the usual shot-noise limit. Furthermore, using such nonlinearities, optical quantum nondemolition measurements can now be carried out at the single-photon level.Comment: 10 pages, 5 figures; Submitted to a Special Issue of J. Opt. B on "Fluctuations and Noise in Photonics and Quantum Optics" (Herman Haus Memorial Issue); v2: minor change

X-Ray Diffraction Reference Intensity Ratios of Amorphous and Poorly Crystalline Phases: Implications for CheMin on the Mars Science Laboratory

The CheMin instrument on the Mars Science Laboratory (MSL) rover Curiosity is an X-ray diffraction (XRD) and X-ray fluorescence (XRF) instrument capable of providing the mineralogical and chemical compositions of rocks and soils on the surface of Mars. CheMin uses a microfocus X-ray tube with a Co target, transmission geometry, and an energy-discriminating X-ray sensitive CCD to produce simultaneous 2-D XRD patterns and energy-dispersive X-ray histograms from powdered samples. Piezoelectric vibration of the cell is used to randomize the sample to reduce preferred orientation effects. Instrument details are provided in [1, 2, 3]. Analyses of rock and soil samples by the Mars Exploration Rovers (MER) show nanophase ferric oxide (npOx) is a significant component of the Martian global soil [4] and is thought to be one of the major contributing phases that the Curiosity rover will encounter if a soil sample is analyzed in Gale Crater. Because of the nature of this material, npOx will likely contribute to an X-ray amorphous or short-order component of a XRD pattern measured by the CheMin instrument

Sub-Shot-Noise Quantum Optical Interferometry: A Comparison of Entangled State Performance within a Unified Measurement Scheme

Phase measurement using a lossless Mach-Zehnder interferometer with certain entangled $N$-photon states can lead to a phase sensitivity of the order of 1/N, the Heisenberg limit. However, previously considered output measurement schemes are different for different input states to achieve this limit. We show that it is possible to achieve this limit just by the parity measurement for all the commonly proposed entangled states. Based on the parity measurement scheme, the reductions of the phase sensitivity in the presence of photon loss are examined for the various input states.Comment: 5 pages, 2 figure