Optimal two-qubit tomography based on local and global measurements: Maximal robustness against errors as described by condition numbers
Optimal two-qubit tomography based on local and global measurements: Maximal robustness against errors as described by condition numbers
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DOI：
10.1103/physreva.90.062123
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发表时间：
2014-09
影响因子：
2.9
通讯作者：
A. Miranowicz;Karol Bartkiewicz;J. Peřina;M. Koashi;N. Imoto;F. Nori
中科院分区：
文献类型：
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作者：
A. Miranowicz;Karol Bartkiewicz;J. Peřina;M. Koashi;N. Imoto;F. Nori
我们提出了一种基于线性反转的重建未知两量子比特态的各种层析协议的误差分析。我们解决了根据Gastinel-Kahan定理所要求的条件数的最小值(即等于1)来寻找对错误最健壮的层析协议的问题。相比之下，标准的断层扫描协议，包括那些基于相互无偏的碱基的协议，对于确定未知的两个量子比特密度矩阵的所有16个元素来说并不是最佳的。我们的方法是基于16个广义Pauli算子的测量，其中12个可以局部测量，另外4个需要非局部Bell测量。我们的方法相当于有选择地逐一测量未知两量子比特密度矩阵的所有实数和虚数元素。我们描述了该协议的两个实验上可行的装置，用于使用常规探测器和线性光学元件最佳地重建处于未知偏振态的两个光子。此外，我们还定义了多量子比特或多能级(QUDIT)系统态的最优重构算符。
We present an error analysis of various tomographic protocols based on the linear inversion for the reconstruction of an unknown two-qubit state. We solve the problem of finding a tomographic protocol which is the most robust against errors in terms of the lowest value (i.e., equal to 1) of a condition number, as required by the Gastinel‐Kahan theorem. In contrast, standard tomographic protocols, including those based on mutually unbiased bases, are nonoptimal for determining all the 16 elements of an unknown two-qubit density matrix. Our method is based on the measurements of the 16 generalized Pauli operators, where twelve of them can be locally measured, and the other four require nonlocal Bell measurements. Our method corresponds to selectively measuring, one by one, all the real and imaginary elements of an unknown two-qubit density matrix. We describe two experimentally feasible setups of this protocol for the optimal reconstruction of two photons in an unknown polarization state using conventional detectors and linear-optical elements. Moreover, we define the operators for the optimal reconstruction of the states of multiqubit or multilevel (qudit) systems.