论文标题
评论“量子计量学的热力学原理”
Comment on "Thermodynamic Principle for Quantum Metrology"
论文作者
论文摘要
在物理中。莱特牧师。 128，200501（2022）作者考虑了量子计量学的热力学成本。主要结果之一是$ \ Mathcal {s} \ geq \ log（2）\ | h_λ\ |^{ - 2} f_q [ψ_λ] $，它声称将最佳测量的shannon熵$ \ Mathcal {s} $（即，根据对称的对数衍生）的量子$ f_q $ f _q $ f _q $ fulgarithmic衍生）$ | | | | |但是，我们表明，在作者考虑的设置中，我们有$ \ Mathcal {s} = \ log（2）$和$ \ | | h_λ\ |^{2} = \ max_ {ψ_λ} f_q [ψ_λ] $，以便它们的不等式减少到微不足道的不等式$ \ max_ {ψ_λ} f_q [ψ_λ] 信息。此外，对于纯状态量子计量学，存在最佳测量值（尽管不是基于对称对数导数），$ 0 \ leq \ leq \ Mathcal {s} \ leq \ log（2）$，导致某些状态$ |ψ_λ\ rangle $的不平等。
In Phys. Rev. Lett. 128, 200501 (2022) the authors consider the thermodynamic cost of quantum metrology. One of the main results is $\mathcal{S} \geq \log(2) \| h_λ\|^{-2} F_Q [ψ_λ]$, which purports to relate the Shannon entropy $\mathcal{S}$ of an optimal measurement (i.e., in the basis of the symmetric logarithmic derivative) to the quantum Fisher information $F_Q$ of the pure state $|ψ_λ\rangle$. However, we show that in the setting considered by the authors we have $\mathcal{S} = \log(2)$ and $\| h_λ\|^{2} = \max_{ψ_λ} F_Q[ψ_λ]$, so that their inequality reduces to the trivial inequality $\max_{ψ_λ} F_Q[ψ_λ] \geq F_Q[ψ_λ]$, and does not in fact relate the entropy $\mathcal{S}$ to the quantum Fisher information. Moreover, for pure state quantum metrology, there exist optimal measurements (though not in the basis of the symmetric logarithmic derivative) for which $0 \leq \mathcal{S} \leq \log(2)$, leading to violations of the inequality for some states $|ψ_λ\rangle$.
