There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

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The Observation of Gravitational Waves from a Binary Black Hole Merger

From the Publisher: 
The accessible presentation of this book gives both a general view of the entire computer vision enterprise and also offers sufficient detail to be able to build useful applications. Users learn techniques that have proven to be useful by first-hand experience and a wide range of mathematical methods. A CD-ROM with every copy of the text contains source code for programming practice, color images, and illustrative movies. Comprehensive and up-to-date, this book includes essential topics that either reflect practical significance or are of theoretical importance. Topics are discussed in substantial and increasing depth. Application surveys describe numerous important application areas such as image based rendering and digital libraries. Many important algorithms broken down and illustrated in pseudo code. Appropriate for use by engineers as a comprehensive reference to the computer vision enterprise.

Computer vision : a modern approach = 计算机视觉 : 一种现代的方法

Researchers demonstrate the ability to multiplex and transfer data between twisted beams of light with different amounts of orbital angular momentum — a development that provides new opportunities for increasing the data capacity of free-space optical communications links.

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Terabit free-space data transmission employing orbital angular momentum multiplexing

Previous analyses of conditional \\phi-phase gates for photonic qubits that treat cross-phase modulation (XPM) in a causal, multimode, quantum field setting suggest that a large (~\\pi rad) nonlinear phase shift is always accompanied by fidelity-degrading noise [J. H. Shapiro, Phys. Rev. A 73, 062305 (2006); J. Gea-Banacloche, Phys. Rev. A 81, 043823 (2010)]. Using an atomic V-system to model an XPM medium, we present a conditional phase gate that, for sufficiently small nonzero \\phi, has high fidelity. The gate is made cascadable by using using a special measurement, principal mode projection, to exploit the quantum Zeno effect and preclude the accumulation of fidelity-degrading departures from the principal-mode Hilbert space when both control and target photons illuminate the gate.

Deterministic and cascadable conditional phase gate for photonic qubits

Time-energy high-dimensional quantum key distribution (HD-QKD) leverages the high-dimensional nature of time-energy entangled biphotons and the loss tolerance of single-photon detection to achieve long-distance key distribution with high photon information efficiency. To date, the general-attack security of HD-QKD has only been proven in the asymptotic regime, while HD-QKD's finite-key security has only been established for a limited set of attacks. Here we fill this gap by providing a rigorous HD-QKD security proof for general attacks in the finite-key regime. Our proof relies on an entropic uncertainty relation that we derive for time and conjugate-time measurements that use dispersive optics, and our analysis includes an efficient decoy-state protocol in its parameter estimation. We present numerically evaluated secret-key rates illustrating the feasibility of secure and composable HD-QKD over metropolitan-area distances when the system is subjected to the most powerful eavesdropping attack.

/pdf/finite-key-analysis-for-time-energy-high-dimensional-quantum-3zwf5y9q8r.pdf

Finite-key analysis for time-energy high-dimensional quantum key distribution

We present a theoretical study of minimum error probability discrimination, using quantum-optical probe states, of M optical phase shifts situated symmetrically on the unit circle. We assume ideal lossless conditions and full freedom for implementing quantum measurements and for probe-state selection, subject only to a constraint on the average energy, i.e., photon number. In particular, the probe state is allowed to have any number of signal and ancillary modes and to be pure or mixed. Our results are based on a simple criterion that partitions the set of pure probe states into equivalence classes with the same error probability performance. Under an energy constraint, we find the explicit form of the state that minimizes the error probability. This state is an unentangled but nonclassical single-mode state. The error performance of the optimal state is compared with several standard states in quantum optics. We also show that discrimination with zero error is possible only beyond a threshold energy of (M − 1)/2. For the M = 2 case, we show that the optimum performance is readily demonstrable with current technology. While transmission loss and detector inefficiencies lead to a nonzero erasure probability, the error rate conditional on no erasure is shown to remain the same as the optimal lossless error rate.

Symmetric M-ary phase discrimination using quantum-optical probe states

We describe our efforts to observe squeezing, and related nonclassical effects, in three forward four-wave mixing experiments using sodium vapor as a nonlinear medium. In a single-beam experiment with homodyne detection, we found optically phase-sensitive noise, which was radio-frequency phase insensitive, in a cw dye-laser beam that had propagated through sodium vapor. The minima of the phase-sensitive noise were always at or above the coherent-state value. In our forward four-wave mixing experiment with probe–conjugate-beam direct detection and correlation, we found that the sodium-vapor interaction produced positive noise correlation between the probe and conjugate beams. The correlation, however, did not exceed the excess noises on these beams, so that a nonclassical behavior was not demonstrated. Finally, our forward four-wave mixing experiment with probe–conjugate-beam combination and homodyne detection did demonstrate the generation of squeezed-state light in our setup. Optically phase-sensitive noise with a minimum falling 4% below the coherent-state level was observed.

Squeezing experiments in sodium vapor

The locking effect is a phenomenon which is unique to quantum information theory and represents one of the strongest separations between the classical and quantum theories of information. The Fawzi-Hayden-Sen (FHS) locking protocol harnesses this effect in a cryptographic context, whereby one party can encode n bits into n qubits while using only a constant-size secret key. The encoded message is then secure against any measurement that an eavesdropper could perform in an attempt to recover the message, but the protocol does not necessarily meet the composability requirements needed in quantum key distribution applications. In any case, the locking effect represents an extreme violation of Shannon's classical theorem, which states that information-theoretic security holds in the classical case if and only if the secret key is the same size as the message. Given this intriguing phenomenon, it is of practical interest to study the effect in the presence of noise, which can occur in the systems of both the legitimate receiver and the eavesdropper. This paper formally defines the locking capacity of a quantum channel as the maximum amount of locked information that can be reliably transmitted to a legitimate receiver by exploiting many independent uses of a quantum channel and an amount of secret key sublinear in the number of channel uses. We provide general operational bounds on the locking capacity in terms of other well-known capacities from quantum Shannon theory. We also study the important case of bosonic channels, finding limitations on these channels' locking capacity when coherent-state encodings are employed and particular locking protocols for these channels that might be physically implementable.

Jeffrey H. Shapiro

Papers

Deterministic and cascadable conditional phase gate for photonic qubits

Finite-key analysis for time-energy high-dimensional quantum key distribution

Symmetric M-ary phase discrimination using quantum-optical probe states

Squeezing experiments in sodium vapor

Quantum enigma machines and the locking capacity of a quantum channel