Detecting correlated errors in state-preparation-and-measurement tomography
Detecting correlated errors in state-preparation-and-measurement tomography
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DOI：
10.1103/physreva.92.042312
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发表时间：
2015-10-12
影响因子：
2.9
通讯作者：
van Enk, S. J.
中科院分区：
文献类型：
--
作者：
Jackson, Christopher;van Enk, S. J.
然而，在标准量子态断层扫描中，人们通过对已知设备进行各种测量来估计未知状态，而在探测器断层扫描中，人们通过对测量设备施加各种已知状态来估计测量设备的正算子值测量元素，我们在这里考虑SPAM（状态准备和测量）断层扫描的情况，其中状态和测量设备都是已知的。对于由d-结果探测器测量的d维系统，我们发现，无论未知状态和未知设备的数量如何，最多有d(2)（d(2) - 1）个“规范”参数无法通过任何此类实验确定。对于d = 2的情况，我们发现可以通过实验直接访问的规范不变量，并且可以用来检测和描述SPAM错误。特别是，我们确定了违反SPAM错误之间存在相关性的条件。从SPAM层析成像的角度来看，标准量子态层析成像和探测器层析成像都是通过假设已知一组基准测量值或已知一组基准状态来固定测量参数的协议。
Whereas in standard quantum-state tomography one estimates an unknown state by performing various measurements with known devices, and whereas in detector tomography one estimates the positive-operator-valued-measurement elements of a measurement device by subjecting to it various known states, we consider here the case of SPAM (state preparation and measurement) tomography where neither the states nor the measurement device are assumed known. For d-dimensional systems measured by d-outcome detectors, we find there are at most d(2)(d(2) - 1) "gauge" parameters that can never be determined by any such experiment, irrespective of the number of unknown states and unknown devices. For the case d = 2 we find gauge-invariant quantities that can be accessed directly experimentally and that can be used to detect and describe SPAM errors. In particular, we identify conditions whose violations detect the presence of correlations between SPAM errors. From the perspective of SPAM tomography, standard quantum-state tomography and detector tomography are protocols that fix the gauge parameters through the assumption that some set of fiducial measurements is known or that some set of fiducial states is known, respectively.