Multiparameter estimation for qubit states with collective measurements: a case study
Multiparameter estimation for qubit states with collective measurements: a case study
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DOI：
10.1088/1367-2630/ac599d
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发表时间：
2022-03-01
影响因子：
3.3
通讯作者：
Len, Yink Loong
中科院分区：
文献类型：
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作者：
Len, Yink Loong
涉及多参数的量子估计仍然是一个重要的理论和实践问题。在这项工作中，我们研究了同时估计两个参数的问题，这两个参数分别与Bloch矢量的长度和方向相关联，其中为了获得两个参数的最佳估计精度，需要在多个量子位上进行集体测量。将N个量子比特作为自旋-1/2系统的集合，我们证明了两个参数的同时最优估计可以用一个简单的集体测量策略渐近地获得——首先，我们通过测量不同总角动量值j对应的空间中的种群来估计长度参数，然后我们通过在最优基上执行自旋投影来估计方向参数。进一步，我们证明了当状态接近纯态时，对于足够大但不是任意大的N，大多数信息将在最大的三个j子空间中被捕获。然后，我们研究了如何通过观察贝尔多端口设置的输出签名来实现总角动量测量，无论是精确地为N = 2,3，还是近似地为其他N值的量子位几乎纯时。我们还获得了数值结果，表明使用Bell多端口设置，可以根据输出处各自的干扰特征区分在j = N/2和j = N/2 - 1子空间上的投影。
Quantum estimation involving multiple parameters remains an important problem of both theoretical and practical interest. In this work, we study the problem of simultaneous estimation of two parameters that are respectively associate with the length and direction of the Bloch vector for identically prepared qubit states that is confined to a plane, where in order to obtain the optimal estimation precision for both parameters, collective measurements on multiple qubits are necessary. Upon treating N qubits as an ensemble of spin-1/2 systems, we show that simultaneous optimal estimation for both parameters can be attained asymptotically with a simple collective measurement strategy-first, we estimate the length parameter by measuring the populations in spaces corresponding to different total angular momentum values j, then we estimate the direction parameter by performing a spin projection onto an optimal basis. Furthermore, we show that when the state is nearly pure, for sufficiently but not arbitrarily large N, most information will be captured in the largest three j-subspaces. Then, we study how the total angular-momentum measurement can be realized by observing output signatures from a Bell multiport setup, either exactly for N = 2, 3, or approximately when the qubits are nearly pure for other N values. We also obtain numerical results that suggest that using a Bell multiport setup, one can distinguish between projection onto the j = N/2 and j = N/2 - 1 subspaces from their respective interference signatures at the output.