论文标题
使用半决赛编程在量子计量学和纠缠理论中优化
Optimization in quantum metrology and entanglement theory using semidefinite programming
论文作者
论文摘要
我们讨论有效的方法，以优化两分量子系统中当地哈密顿量的计量性能。对于给定的量子状态，我们的方法找到了最佳的本地哈密顿量，该国家的表现可分开的状态与量子计量学的角度最大。我们表明，可以减少此问题，以最大程度地利用一组哈密顿人的量子渔民信息。我们以双线性形式介绍量子渔民信息，并通过迭代的远见（ISS）方法最大化它，其中每个步骤均基于半决赛编程。我们还通过对较小系统效果很好的时刻方法解决了问题。我们考虑量子信息理论中的许多其他问题，这些问题可以以类似的方式解决。例如，我们确定绑定的纠缠量子状态最大程度地违反了可计算的交叉标准（CCNR）标准。我们的方法是一种有效的方法之一，可用于优化量子计量学中统一动力学，其他方法是，例如机器学习，变异量子电路或神经网络。我们方法的优点是由于该方法的简单数学结构，快速而稳健的收敛性。
We discuss efficient methods to optimize the metrological performance over local Hamiltonians in a bipartite quantum system. For a given quantum state, our methods find the best local Hamiltonian for which the state outperforms separable states the most from the point of view of quantum metrology. We show that this problem can be reduced to maximize the quantum Fisher information over a certain set of Hamiltonians. We present the quantum Fisher information in a bilinear form and maximize it by an iterative see-saw (ISS) method, in which each step is based on semidefinite programming. We also solve the problem with the method of moments that works very well for smaller systems. We consider a number of other problems in quantum information theory that can be solved in a similar manner. For instance, we determine the bound entangled quantum states that maximally violate the Computable Cross Norm-Realignment (CCNR) criterion. Our approach is one of the efficient methods that can be applied for an optimization of the unitary dynamics in quantum metrology, the other methods being, for example, machine learning, variational quantum circuits, or neural networks. The advantage of our method is the fast and robust convergence due to the simple mathematical structure of the approach.
