Fisher information under decoherence in Bloch representation
Fisher information under decoherence in Bloch representation
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Bloch 表示中退相干下的 Fisher 信息
DOI：
10.1103/physreva.87.022337
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发表时间：
2013-02-25
影响因子：
2.9
通讯作者：
Nori, Franco
中科院分区：
文献类型：
--
作者：
Zhong, Wei;Sun, Zhe;Nori, Franco
从几何角度研究了退相干下量子费希尔信息的两种变体的动力学。我们首先根据布洛赫向量推导单个量子位的这两个量的显式公式。此外，我们还获得了它们在三个不同退相干通道下的解析结果，并将其表示为仿射变换矩阵。使用层次方程方法，我们对耗散模型中两组信息的动力学进行数值研究，并将数值结果与应用旋转波近似获得的解析结果进行比较。我们通过在李代数 su(d) 的一组公共生成器中扩展密度矩阵和厄米算子，进一步用 qudit 的布洛赫向量来表达这两个信息量。通过计算动态量子Fisher信息，我们发现碰撞相移显着降低了拉姆齐干涉测量相位参数的精度。
The dynamics of two variants of quantum Fisher information under decoherence is investigated from a geometrical point of view. We first derive the explicit formulas of these two quantities for a single qubit in terms of the Bloch vector. Moreover, we obtain analytical results for them under three different decoherence channels, which are expressed as affine transformation matrices. Using the hierarchy equation method, we numerically study the dynamics of both sets of information in a dissipative model and compare the numerical results with the analytical ones obtained by applying the rotating-wave approximation. We further express the two information quantities in terms of the Bloch vector for a qudit by expanding the density matrix and Hermitian operators in a common set of generators of the Lie algebra su(d). By calculating the dynamical quantum Fisher information, we find that the collisional dephasing significantly diminishes the precision of the phase parameter with the Ramsey interferometry.