论文标题
平价量子态之间的量子假设检验
Quantum hypothesis testing between qubit states with parity
论文作者
论文摘要
量子假设检验（QHT）提供了一种有效的方法，可以使用两种结果阳性算子值测量（POVM）区分两个量子状态。 QHT中可能发生两种决策错误。在本文中，我们关注QHT的不对称设置，在考虑到由于缺乏手性参考框架引起的操作局限性，对两种决策误差进行了不平等的处理。此参考框架与由身份转换和奇偶校验转换组成的组$ \ bbz_2 $关联。因此，我们必须仅执行$ \ bbz_2 $ invariant povms来区分两个量子状态。我们从两个纯状态之间的歧视开始。通过解决特定的优化问题，我们完全表征了II型误差的最小概率的渐近行为，而II误差的最小概率是在错误假设时发生的。我们的结果表明，如果此类两个纯状态的$ \ bbz_2 $ - twirlings不同，则最小概率在有限数量的副本中降低至零。我们进一步得出了临界数量的副本数量，以使最小概率减少到零。最后，我们用最大混合状态替换了两个纯状态之一，并类似地表征了II型误差的最小概率的渐近行为。
Quantum hypothesis testing (QHT) provides an effective method to discriminate between two quantum states using a two-outcome positive operator-valued measure (POVM). Two types of decision errors in a QHT can occur. In this paper we focus on the asymmetric setting of QHT, where the two types of decision errors are treated unequally, considering the operational limitations arising from the lack of a reference frame for chirality. This reference frame is associated with the group $\bbZ_2$ consisting of the identity transformation and the parity transformation. Thus, we have to discriminate between two qubit states by performing the $\bbZ_2$-invariant POVMs only. We start from the discrimination between two pure states. By solving the specific optimization problem we completely characterize the asymptotic behavior of the minimal probability of type-II error which occurs when the null hypothesis is accepted when it is false. Our results reveal that the minimal probability reduces to zero in a finite number of copies, if the $\bbZ_2$-twirlings of such two pure states are different. We further derive the critical number of copies such that the minimal probability reduces to zero. Finally, we replace one of the two pure states with a maximally mixed state, and similarly characterize the asymptotic behavior of the minimal probability of type-II error.
