论文标题
掩盖在纯状态和混合状态中编码的量子信息
Masking quantum information encoded in pure and mixed states
论文作者
论文摘要
量子信息的掩盖意味着信息隐藏在子系统中并分布在复合系统上。 Modi等。在[Phys。莱特牧师。 120，230501（2018）]认为，对于某些有限的非正交量子状态，这是正确的，并且任意量子状态不可能。在本文中，我们分别讨论了掩盖纯净和混合状态中编码的量子信息的问题。基于一组纯状态被操作员掩盖的必要条件，我们发现存在一组无法掩盖的四个状态，这意味着不可能掩盖未知的纯状态。我们构建了一个蒙版$ s^\ sharp $，并获得其最大掩盖套件，从而对上述莫迪论文提出的猜想产生了肯定的答案。我们还证明，纯状态的正交（线性独立）子集可以通过等轴测图（分别注射）掩盖。概括纯状态的情况，我们介绍了一组混合状态的掩模性，并证明可以通过等距$ s^{\ diamond} $掩盖混合状态的通勤子集，而任何操作员都无法掩盖所有混合状态。我们还发现异构体的混合状态$ {s^{\ sharp}} $和$ {s^{\ diamond}} $的最大掩膜。
Masking of quantum information means that information is hidden from a subsystem and spread over a composite system. Modi et al. proved in [Phys. Rev. Lett. 120, 230501 (2018)] that this is true for some restricted sets of nonorthogonal quantum states and it is not possible for arbitrary quantum states. In this paper, we discuss the problem of masking quantum information encoded in pure and mixed states, respectively. Based on an established necessary and sufficient condition for a set of pure states to be masked by an operator, we find that there exists a set of four states that can not be masked, which implies that to mask unknown pure states is impossible. We construct a masker $S^\sharp$ and obtain its maximal maskable set, leading to an affirmative answer to a conjecture proposed in Modi's paper mentioned above. We also prove that an orthogonal (resp. linearly independent) subset of pure states can be masked by an isometry (resp. injection). Generalizing the case of pure states, we introduce the maskability of a set of mixed states and prove that a commuting subset of mixed states can be masked by an isometry $S^{\diamond}$ while it is impossible to mask all of mixed states by any operator. We also find the maximal maskable sets of mixed states of the isometries ${S^{\sharp}}$ and ${S^{\diamond}}$, respectively.
