Testing Partial Instrument Monotonicity

When multi-dimensional instruments are used to identify and estimate causal effects, the monotonicity condition may not hold due to heterogeneity in the population. Under a partial monotonicity condition, which only requires the monotonicity to hold for each instrument separately holding all the other instruments fixed, the 2SLS estimand can still be a positively weighted average of LATEs. In this paper, we provide a simple nonparametric test for partial instrument monotonicity. We demonstrate the good finite sample properties of the test through Monte Carlo simulations. We then apply the test to monetary incentives and distance from results centers as instruments for the knowledge of HIV status

Implications of supermassive neutron stars for the form of the equation of state of hybrid stars

The observations of PSR J0952-0607 and the second object in GW190814 event indicate the possible existence of supermassive neutron stars. In this work, by using the Constant-Sound-Speed (CSS) parametrization to describe the equation of state (EOS) of quark matter, the constraints on the EOS parameters from supermassive hybrid stars are investigated through the Maxwell and Gibbs constructions. It is shown that to support a supermassive hybrid star, a lower transition energy density, a smaller energy density discontinuity and a higher sound speed of quark matter are favored. For the constructed hybrid star EOS model, the maximum mass of the corresponding hybrid stars will not meet the lower mass limit of the second object in GW190814 if the energy density discontinuity takes a value higher than $180~{\rm MeV~fm^{-3}}$. Moreover, it is confirmed that the supermassive neutron star observation can also rule out the existence of twin stars as a supermassive hybrid star requires a relatively small energy density discontinuity. Finally, we give a rough estimate of the lower limit of the dimensionless tidal deformability of neutron stars which ranges from 2 to 3.Comment: 12 pages, 5 figure

Numerical Security Analysis of Three-State Quantum Key Distribution Protocol with Realistic Devices

Quantum key distribution (QKD) is a secure communication method that utilizes the principles of quantum mechanics to establish secret keys. The central task in the study of QKD is to prove security in the presence of an eavesdropper with unlimited computational power. In this work, we successfully solve a long-standing open question of the security analysis for the three-state QKD protocol with realistic devices, i,e, the weak coherent state source. We prove the existence of the squashing model for the measurement settings in the three-state protocol. This enables the reduction of measurement dimensionality, allowing for key rate computations using the numerical approach. We conduct numerical simulations to evaluate the key rate performance. The simulation results show that we achieve a communication distance of up to 200 km.Comment: 14 pages, 5 figure

Hybrid algorithm simulating non-equilibrium steady states of an open quantum system

Non-equilibrium steady states are a focal point of research in the study of open quantum systems. Previous variational algorithms for searching these steady states have suffered from resource-intensive implementations due to vectorization or purification of the system density matrix, requiring large qubit resources and long-range coupling. In this work, we present a novel variational quantum algorithm that efficiently searches for non-equilibrium steady states by simulating the operator-sum form of the Lindblad equation. By introducing the technique of random measurement, we are able to estimate the nonlinear cost function while reducing the required qubit resources by half compared to previous methods. Additionally, we prove the existence of the parameter shift rule in our variational algorithm, enabling efficient updates of circuit parameters using gradient-based classical algorithms. To demonstrate the performance of our algorithm, we conduct simulations for dissipative quantum transverse Ising and Heisenberg models, achieving highly accurate results. Our approach offers a promising solution for effectively addressing non-equilibrium steady state problems while overcoming computational limitations and implementation challenges.Comment: 8 pages, 4 figure

The TIPE Model for Teaching Technology-Based Entrepreneurship

It is widely believed that the technology-based entrepreneurship has great potential to increase wealth and competitiveness. Researchers believe that Technology-based Entrepreneurship Education (TEE) may raise students’ awareness about the technology entrepreneurship and the opportunities for technology commercialization. However, TEE has a relatively shorter history than conventional entrepreneurship education in business schools and there are fewer cases. This paper will use a revised 4W1H framework to review existing models of TEE and then present the TIPE model that has been implemented at a university in Hong Kong since 2001 for master students. Educational and policy implications are explored finally

A hybrid algorithm for quadratically constrained quadratic optimization problems

Quadratically Constrained Quadratic Programs (QCQPs) are an important class of optimization problems with diverse real-world applications. In this work, we propose a variational quantum algorithm for general QCQPs. By encoding the variables on the amplitude of a quantum state, the requirement of the qubit number scales logarithmically with the dimension of the variables, which makes our algorithm suitable for current quantum devices. Using the primal-dual interior-point method in classical optimization, we can deal with general quadratic constraints. Our numerical experiments on typical QCQP problems, including Max-Cut and optimal power flow problems, demonstrate a better performance of our hybrid algorithm over the classical counterparts.Comment: 8 pages, 3 figure