Coherence measures based on sandwiched Rényi relative entropy

Coherence is a fundamental ingredient for quantum physics and a key resource for quantum information theory.Baumgratz,Cramer and Plenio established a rigorous framework(BCP framework)for quantifying coherence[Baumgratz T,Cramer M and Plenio M B Phys.Rev.Lett.113140401(2014)].In the present paper,under the BCP framework we provide two classes of coherence measures based on the sandwiched Rényi relative entropy.We also prove that we cannot get a new coherence measure f(C(·))by a function f acting on a given coherence measure C.

Correction of the second-order degree of coherence measurement

The measurement of the second-order degree of coherence [g（2）（t）] is one of the important methods used to study the dynamical evolution of photon-matter interaction systems. Here, we use a nitrogen-vacancy center in a diamond to compare the measurement of g（2） （t） with two methods. One is the prototype measurement process with a tunable delay. The other is a start-stop process based on the time-to-amplitude conversion （TAC） and multichannel analyzer （MCA） system, which is usually applied to achieve efficient measurements. The divergence in the measurement results is observed when the delay time is comparable with the mean interval time between two neighboring detected photons. Moreover, a correction function is presented to correct the results from the TAC-MCA system to the genuine g（2）（t）. Such a correction method will provide a way to study the dynamics in photonic systems for quantum information techniques.

A distributed optical fiber sensing system for synchronous vibration and loss measurement

We propose a fully distributed fusion system combining phase-sensitive optical time-domain reflectometry(Φ-OTDR) and OTDR for synchronous vibration and loss measurement by setting an ingenious frequency sweep rate(FSR) of the optical source. The relationships between FSR, probe pulse width and repeat period are given to balance the amplitude fluctuation of OTDR traces, the dead zone probability and the measurable frequency range of vibration events. In the experiment, we achieve synchronous vibration and loss measurement with FSR of 40 MHz/s, the proble pulse width of 100 ns and repeat rate of 0.4 ms. The fluctuation of OTDR trace is less than 0.45 dB when the signalto-noise ratio(SNR) is over 12 dB for a captured vibration event located at 9.1 km. The proposed method can be used for not only detection but also early warning of damage events in optical communication networks.

Conditional coherent risk measures and regime-switching conic pricing

This paper introduces and represents conditional coherent risk measures as essential suprema of conditional expectations over a convex set of probability measures and as distorted expectations given a concave distortion function.A model is then developed for the bid and ask prices of a European-type asset by a conic formulation.The price process is governed by a modified geometric Brownian motion whose drift and diffusion coefficients depend on a Markov chain.The bid and ask prices of a European-type asset are then characterized using conic quantization.

Measurement of the degree of temporal coherence of unpolarized light beams

We measure the electromagnetic degree of temporal coherence and the associated coherence time for quasi-monochromatic unpolarized light beams emitted by an LED, a filtered halogen lamp, and a multimode He–Ne laser.The method is based on observing at the output of a Michelson interferometer the visibilities(contrasts) of the intensity and polarization-state modulations expressed in terms of the Stokes parameters. The results are in good agreement with those deduced directly from the source spectra. The measurements are repeated after passing the beams through a linear polarizer so as to elucidate the role of polarization in electromagnetic coherence. While the polarizer varies the equal-time degree of coherence consistently with the theoretical predictions and alters the inner structure of the coherence matrix, the coherence time remains almost unchanged when the light varies from unpolarized to polarized. The results are important in the areas of applications dealing with physical optics and electromagnetic interference.

The pitch-catch nonlinear ultrasonic imaging techniques for structural health monitoring

Nonlinear ultrasonic imaging techniques in pulse-echo configuration have recently shown their potential to allow the effective separation of nonlinear and linear features in a nonlinear image.In this study,two ultrasonic phased arrays are implemented to produce an image of elastic nonlinearity through the parallel-sequential subtraction of the coherently scattered components in the through-transmission acoustic field at the transmission or subharmonic frequency.In parallel mode,a physical focus at each pixel is achieved by firing the transmitters with a predefined delay law.In sequential mode,each transmitter is fired in sequence and all the receivers are employed to capture the data simultaneously.This full matrix captured data can be post-processed and focused synthetically at the target area.The images of parallel focusing and sequential focusing are expected to be linearly identical and hence any differences remained on the subtracted image can be related to the nonlinearities arising from the defects.Therefore,the imaging metric here is defined as the difference between parallel and sequentially focused amplitudes obtained from forward coherently scattered fields at each target point.Additionally,the negative influences due to the instrumentation nonlinearities are investigated by studying the remaining relative phase and amplitude at undamaged pixels.A compensation method is implemented to suppress these noises,significantly enhancing the selectivity of nonlinear scattering features.The proposed techniques are then implemented to monitor fatigue crack growth in order to explore the capability of these methods as measures of elastic nonlinearity induced by different sizes of small closed cracks.The promising results suggest that nonlinear imaging can be used to monitor crack growth and improve the detectability at early stages.

PRODUCTION PLANNING PROBLEM WITH PRICING UNDER RANDOM YIELD:CVAR CRITERION

In this paper, we address a basic production planning problem with price dependent demand and stochastic yield of production. We use price and target quantity as decision variables to lower the risk of low yield. The value of risk control becomes more important especially for products with short life cycle. This is because, the profit implications of low yield might be unbearable in the short run. We apply Conditional Value at Risk （CVaR） to model the, risk. CVaR measure is a coherent risk measure and thereby having nice conceptual and mathematical underpinnings. It is also widely used in practice. We consider the problem under general demand function and general distribution function of yield and find sufficient conditions under which the problem has a unique local maximum. We also both analytically and numerically analyze the impact of parameter change on the optimal solution. Among our results, we analytically show that with increasing risk aversion, the optimal price increases. This relation is opposite to that of in Newsvendor problem where the uncertainty lies in demand side.

Estimation on Geometric Measure of Quantum Coherence

We study the geometric measure of quantum coherence recently proposed in [Phys. Rev. Lett. 115(2015)020403]. Both lower and upper bounds of this measure are provided. These bounds are shown to be tight for a class of important coherent states—maximally coherent mixed states. The trade-off relation between quantum coherence and mixedness for this measure is also discussed.

Dynamics of coherence-induced state ordering under Markovian channels

We study the dynamics of coherence-induced state ordering under incoherent channels, particularly four specific Markovian channels： amplitude damping channel, phase damping channel, depolarizing channel and bit flit channel for single-qnbit states. We show that the amplitude damping channel, phase damping channel, and depolarizing channel do not change the coherence-induced state ordering by l1 norm of coherence, relative entropy of coherence, geometric measure of coherence, and Tsallis relative α-entropies, while the bit flit channel does change for some special cases.

Block-coherence measures and coherence measures based on positive-operator-valued measures

We study block-coherence measures based on the resource theory of block-coherence and coherence measures based on positive-operator-valued measures(POVM).Several blockcoherence measures are presented,including the block-coherence measure based on maximum relative entropy,the one-shot block-coherence cost under maximally block-incoherent operations,and the coherence measure based on coherent rank.Their relationships are obtained.Moreover,we describe the deterministic coherence dilution process by constructing blockincoherent operations.Based on the POVM coherence resource theory,we also propose two coherence measures and analyze their relationship.

Correlation-induced coherence and its use in detecting quantum phase transitions

The past two decades have witnessed a surge of interest in exploring correlation and coherence measures to investigate quantum phase transitions(QPTs). Here, motivated by the continued push along this direction, we propose a measure which is built upon the so-called degree of coherence, and advocate using the susceptibility of our measure to detect QPTs. We show that our measure can capture both the notions of coherence and correlations exhibited in bipartite states and therefore represents a hybrid of these two notions. Through examining the XXZ model and the Kitaev honeycomb model, we demonstrate that our measure is favorable for detecting QPTs in comparison to many previous proposals.

Stochastic Control for Optimal Execution:Fast Approximation Solution Scheme Under Nested Mean-semi Deviation and Conditional Value at Risk

When executing a large order of stocks in a market,one important factor in forming the optimal trading strategy is to consider the price impact of large-volume trading activity.Minimizing a risk measure of the implementation shortfall,i.e.,the difference between the value of a trader’s initial equity position and the sum of cash flow he receives from his trading process,is essentially a stochastic control problem.In this study,we investigate such a practical problem under a dynamic coherent risk measure in a market in which the stock price dynamics has a feature of momentum effect.We develop a fast approximation solution scheme,which is critical in highfrequency trading.We demonstrate some prominent features of our derived solution algorithm in providing useful guidance for real implementation.

Dual representation of expectile-based expected shortfall and its properties

An expectile can be considered a generalization of a quantile.While expected shortfall is a quantile-based risk measure,we study its counterpart-the expectile-based expected shortfall-where expectile takes the place of a quantile.We provide its dual representation in terms of a Bochner integral.Among other properties,we show that it is bounded from below in terms of the convex combination of expected shortfalls,and also from above by the smallest law invariant,coherent,and comonotonic risk measures,for which we give the explicit formulation of the corresponding distortion function.As a benchmark to the industry standard expected shortfall,we further provide its comparative asymptotic behavior in terms of extreme value distributions.Based on these results,we finally explicitly compute the expectile-based expected shortfall for selected classes of distributions.

Path-dependent backward stochastic Volterra integral equations with jumps,differentiability and duality principle

We study the existence and uniqueness of a solution to path-dependent backward stochastic Volterra integral equations(BSVIEs)with jumps,where path-dependence means the dependence of the free term and generator of a path of a c`adl`ag process.Furthermore,we prove path-differentiability of such a solution and establish the duality principle between a linear path-dependent forward stochastic Volterra integral equation(FSVIE)with jumps and a linear path-dependent BSVIE with jumps.As a result of the duality principle we get a comparison theorem and derive a class of dynamic coherent risk measures based on path-dependent BSVIEs with jumps.