论文标题
具有任意对称性的参数化密度运算符，以在量子状态估计中获得优势
Parameterizing density operators with arbitrary symmetries to gain advantage in quantum state estimation
论文作者
论文摘要
在这项工作中，我们展示了如何参数化具有任意对称性的密度矩阵，知道Lie代数的发生器（如果对称组是连接的Lie组）或其基础组的发生器（以防有限）。这允许构成Maxent和Maxlik估计技术作为凸优化问题，并大大减少所涉及的函数参数数量。这意味着，除了在减少空间中进行优化的事实外，还可以减少对密度矩阵的良好估计所需的实验数据量。此外，我们运行数值实验，并将这些参数化应用于具有不同对称性的状态的量子状态估计。
In this work, we show how to parameterize a density matrix that has an arbitrary symmetry, knowing the generators of the Lie algebra (if the symmetry group is a connected Lie group) or the generators of its underlying group (in case it is finite). This allows to pose MaxEnt and MaxLik estimation techniques as convex optimization problems with a substantial reduction in the number of parameters of the function involved. This implies that, apart from a computational advantage due to the fact that the optimization is performed in a reduced space, the amount of experimental data needed for a good estimation of the density matrix can be reduced as well. In addition, we run numerical experiments and apply these parameterizations to quantum state estimation of states with different symmetries.
