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Zihao Li

Publications and source records attributed to Zihao Li.

257 records · Page 15Linked to original sources
arXiv2019

Efficient verification of bipartite pure states

We propose practical and efficient protocols for verifying bipartite pure states for any finite dimension, which can also be applied to fidelity estimation. Our protocols are based on adaptive local projective measurements with either one-way or two-way communications, which are very easy to implement in practice. They can extract the key information much more efficiently than known protocols based on tomography or direct fidelity estimation, and their efficiencies are comparable to the best protocols based on entangling measurements. These protocols highlight the significance of mutually unbiased bases (MUBs) and complex projective 2-designs in quantum state verification and fidelity estimation. Moreover, our protocols can be applied to the adversarial scenario, in which states are controlled by a malicious adversary. In this case, surprisingly, one of our protocols based on local measurements is even optimal among protocols without locality restriction.

quant-ph↗
arXiv2019

Implicit Progressive-Iterative Approximation for Curve and Surface Reconstruction

Implicit curve and surface reconstruction attracts the attention of many researchers and gains a wide range of applications, due to its ability to describe objects with complicated geometry and topology. However, extra zero-level sets or spurious sheets arise in the reconstruction process makes the reconstruction result challenging to be interpreted and damage the final result. In this paper, we proposed an implicit curve and surface reconstruction method based on the progressive-iterative approximation method, named implicit progressive-iterative approximation (I-PIA). The proposed method elegantly eliminates the spurious sheets naturally without requiring any explicit minimization procedure, thus reducing the computational cost greatly and providing high-quality reconstruction results. Numerical examples are provided to demonstrate the efficiency and effectiveness of the proposed method.

math.NA↗
arXiv2019

Implementation of generalized measurements on a qudit via quantum walks

Quantum measurements play a fundamental role in quantum mechanics and quantum information processing, but it is not easy to implement generalized measurements, the most powerful measurements allowed by quantum mechanics. Here we propose a simple recipe for implementing generalized measurements on a qudit via quantum walks. With this recipe, any discrete quantum measurement can be implemented via a one-dimensional discrete quantum walk; the number of steps is only two times the number of measurement outcomes. As an illustration, we present a unified solution for implementing arbitrary symmetric informationally complete measurements in dimension 3.

quant-ph↗
arXiv2017

A Distributed Power Routing Method between Regional Markets based on Bellman-Ford Algorithm

With the deregulation of power industry, large power users can buy electricity directly from power producers. For trades between different regional markets, it is necessary to research on the method to find the cheapest route for power exchanging. Moreover, as there exists no coordinator above regional markets, the power routing problem must be solved in a distributed way. Most previous research are based on power electronic transformers. Some research proposed EMS of sub-networks as energy routers, but failed to consider the power flow constraints or did not converge in some specific cases. Our method is based on the EMS of multiple markets, which saves cost by eliminating expensive electronic transformers and has high efficiency in systems with numerous nodes by considering the regional markets as generalized nodes. We take transmission costs and congestion costs into consideration, and uses Bellman-Ford algorithm to determine the cheapest route for power transmission between different regional markets and make convergence analysis about our algorithm. This method proves effective and convergent when there is no loop among the markets. A four-market loop-free case was used to illustrate the efficiency of the method.

math.OC↗