论文标题
旋转Qudit断层扫描和状态重建错误
Spin qudit tomography and state reconstruction error
论文作者
论文摘要
我们考虑在$ d $级别的自旋qudit上执行量子状态断层扫描的任务，仅使用自旋投影对不同量化轴进行测量。在引入了与球形谐波密切相关的操作员的基础之后，遵守旋转量的旋转对称性之后，我们将量子断层扫描任务映射到球体上信号恢复的经典问题上。 We then provide algorithms with $O(rd^3)$ serial runtime, parallelizable down to $O(rd^2)$, for (i) computing a priori upper bounds on the expected error with which spin projection measurements along $r$ given axes can reconstruct an unknown qudit state, and (ii) estimating a posteriori the statistical error in a reconstructed state.我们的算法激发了一种简单的随机断层扫描协议，为此，我们发现使用更多的测量轴可以带来$ r \ r \ of3d $后高原的实质性好处。
We consider the task of performing quantum state tomography on a $d$-level spin qudit, using only measurements of spin projection onto different quantization axes. After introducing a basis of operators closely related to the spherical harmonics, which obey the rotational symmetries of spin qudits, we map our quantum tomography task onto the classical problem of signal recovery on the sphere. We then provide algorithms with $O(rd^3)$ serial runtime, parallelizable down to $O(rd^2)$, for (i) computing a priori upper bounds on the expected error with which spin projection measurements along $r$ given axes can reconstruct an unknown qudit state, and (ii) estimating a posteriori the statistical error in a reconstructed state. Our algorithms motivate a simple randomized tomography protocol, for which we find that using more measurement axes can yield substantial benefits that plateau after $r\approx3d$.
