论文标题
将量子信息掩盖到三方系统中
Masking quantum information into a tripartite syste
论文作者
论文摘要
由于Modi等人引入了量子信息的掩盖。在[PRL 120，230501（2018）]中，已经发表了许多关于该主题的讨论。 在本文中，我们考虑了量子多部分掩蔽器（QMM）与量子误差校正代码（QECC）之间的关系。我们说，如果所有图像状态$ \ h^{（n）} $可以将系统$ k $的纯状态的子集$ q $掩盖到$ s | c $的所有图像状态$ s |ψ\> $中，则$ s |ψ\> $在$ q $中$ s |ψ\> $在$ q $中具有相同的大小为spystem。我们称这样的$ s $ qmm为$ q $。通过建立QMM的表达，我们获得了QMMS和QECC之间的关系，该QMMS与QMM之间的关系读到，当静脉测定是系统中所有纯状态的QMM时，并且仅当其范围是任何单次呼吸通道的QECC。 As an application, we prove that there is no an isometric universal masker from $\C^2$ into $\C^2\otimes\C^2\otimes\C^2$ and then the states of $\C^3$ can not be masked isometrically into $\C^2\otimes\C^2\otimes\C^2$.这给了主要结果，并在[PRA 98，062306（2018）]中给出了一个否定的答案。另一个应用程序是 $ \ c^d $的任意量子状态可以完全隐藏 在三方系统的任何两个子系统之间的相关性中，$ \ c^{d+1} \ otimes \ c^{d+1} \ otimes \ c^{d+1} $，而任意量子状态不能完全隐藏在bipartite System [prl 98，0808080502（2007）之间的相关性中。
Since masking of quantum information was introduced by Modi et al. in [PRL 120, 230501 (2018)], many discussions on this topic have been published. In this paper, we consider relationship between quantum multipartite maskers (QMMs) and quantum error-correcting codes (QECCs). We say that a subset $Q$ of pure states of a system $K$ can be masked by an operator $S$ into a multipartite system $\H^{(n)}$ if all of the image states $S|ψ\>$ of states $|ψ\>$ in $Q$ have the same marginal states on each subsystem. We call such an $S$ a QMM of $Q$. By establishing an expression of a QMM, we obtain a relationship between QMMs and QECCs, which reads that an isometry is a QMM of all pure states of a system if and only if its range is a QECC of any one-erasure channel. As an application, we prove that there is no an isometric universal masker from $\C^2$ into $\C^2\otimes\C^2\otimes\C^2$ and then the states of $\C^3$ can not be masked isometrically into $\C^2\otimes\C^2\otimes\C^2$. This gives a consummation to a main result and leads to a negative answer to an open question in [PRA 98, 062306 (2018)]. Another application is that arbitrary quantum states of $\C^d$ can be completely hidden in correlations between any two subsystems of the tripartite system $\C^{d+1}\otimes\C^{d+1}\otimes\C^{d+1}$, while arbitrary quantum states cannot be completely hidden in the correlations between subsystems of a bipartite system [PRL 98, 080502 (2007)].
