Quantum state tomography with incomplete data: Maximum entropy and variational quantum tomography
Quantum state tomography with incomplete data: Maximum entropy and variational quantum tomography
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DOI：
10.1103/physreva.87.052140
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发表时间：
2013-05
影响因子：
2.9
通讯作者：
Douglas Soares Gonçalves;C. Lavor;M. A. Gomes-Ruggiero;André T. Cesário;R. Vianna;T. O. Maciel
中科院分区：
文献类型：
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作者：
Douglas Soares Gonçalves;C. Lavor;M. A. Gomes-Ruggiero;André T. Cesário;R. Vianna;T. O. Maciel
每当我们没有完整的测量信息集时，就无法唯一确定量子态的估计。在这种情况下，在与可用数据兼容的密度矩阵中，通常优选最不承诺丢失信息的密度矩阵。这就是最大熵估计 (MaxEnt) 和变分量子断层扫描 (VQT) 的目的。在这里，我们提出了变分量子断层摄影的一种变体，并展示了它与具有不完整测量集的量子断层摄影中的最大熵方法的关系。我们证明了它们在特征基测量情况下的等价性，并通过数值模拟我们强调了它们的相似行为。因此，在修改后的 VQT 公式中，我们对量子态的估计与 MaxEnt 中一样无偏，并且优点是可以通过线性半定程序更有效地求解 VQT。
Whenever we do not have an informationally complete set of measurements, the estimate of a quantum state can not be uniquely determined. In this case, among the density matrices compatible with the available data, it is commonly preferred that one which is the most uncommitted with the missing information. This is the purpose of the Maximum Entropy estimation (MaxEnt) and the Variational Quantum Tomography (VQT). Here, we propose a variant of Variational Quantum Tomography and show its relationship with Maximum Entropy methods in quantum tomographies with incomplete set of measurements. We prove their equivalence in case of eigenbasis measurements, and through numerical simulations we stress their similar behavior. Hence, in the modified VQT formulation we have an estimate of a quantum state as unbiased as in MaxEnt and with the benefit that VQT can be more efficiently solved by means of linear semidefinite programs.