论文标题
检查Schatten-$ p $ norm功能的有效性作为连贯措施
Examining the validity of Schatten-$p$-norm-based functionals as coherence measures
论文作者
论文摘要
不同的作者已经询问了两类schatten- $ p $ - 基于基于$ c_p（ρ）= \ min_ {c_p（ρ）= \ min_ {σ\ in \ mathcal {i}} ||ρ-ρ-= || _p _p $ and $ \ tilde {c} _p} _p（ρ（ρ）是不一致的操作，严格不一致的操作和真正不连贯的操作下的有效连贯措施，其中$ \ Mathcal {i} $是一组不连贯的状态，$Δρ$是密度运算符$ρ$的对角线部分。在这些问题中，我们只知道$ C_P（ρ）$不是不连贯的操作和严格不一致的操作下的有效连贯措施，但是所有其他方面都保持开放。在本文中，我们证明（1）$ \ tilde {c} _1（ρ）$都是在严格不一致的操作和真正不相互不相互不相互的操作下的有效连贯措施$ {c} _ {p> 1}（ρ）$或$ \ tilde {c} _ {p> 1}（ρ）$是三组操作中的任何一个有效的连贯度量。本文不仅提供了$ C_P（ρ）$和$ \ tilde {C} _p（ρ）$作为连贯措施的有效性的彻底检查，而且还找到了一个示例，可以在严格的不连贯操作下实现单调性，但在不连贯的操作下违反了它。
It has been asked by different authors whether the two classes of Schatten-$p$-norm-based functionals $C_p(ρ)=\min_{σ\in\mathcal{I}}||ρ-σ||_p$ and $ \tilde{C}_p(ρ)= \|ρ-Δρ\|_{p}$ with $p\geq 1$ are valid coherence measures under incoherent operations, strictly incoherent operations, and genuinely incoherent operations, respectively, where $\mathcal{I}$ is the set of incoherent states and $Δρ$ is the diagonal part of density operator $ρ$. Of these questions, all we know is that $C_p(ρ)$ is not a valid coherence measure under incoherent operations and strictly incoherent operations, but all other aspects remain open. In this paper, we prove that (1) $\tilde{C}_1(ρ)$ is a valid coherence measure under both strictly incoherent operations and genuinely incoherent operations but not a valid coherence measure under incoherent operations, (2) $C_1(ρ)$ is not a valid coherence measure even under genuinely incoherent operations, and (3) neither ${C}_{p>1}(ρ)$ nor $\tilde{C}_{p>1}(ρ)$ is a valid coherence measure under any of the three sets of operations. This paper not only provides a thorough examination on the validity of taking $C_p(ρ)$ and $\tilde{C}_p(ρ)$ as coherence measures, but also finds an example that fulfills the monotonicity under strictly incoherent operations but violates it under incoherent operations.
