论文标题
与多种用途的未知统一通道的比较
Comparison of unknown unitary channels with multiple uses
论文作者
论文摘要
量子对象的比较是确定两个未知量子对象的任务。它是学习量子对象的学习特性的最基本信息处理任务之一，已经研究了量子状态，量子通道和量子测量结果的比较。通常，量子对象的重复使用提高了比较的成功概率。纯状态比较的最佳策略，即每个未知纯状态的多个副本的量子状态的比较，但是单一比较的最佳策略，对于每个未知单一通道的多次使用的量子通道的比较，由于每个单一通道的复杂性，每个未知单一通道的多次使用情况都不知道。在本文中，我们研究了基于量子测试仪形式主义的单一通道的多种用途的统一比较。我们获得了最佳的最小值和最佳的明确比较策略，以统一比较两个未知$ D $ d $ dimensional的单一频道$ u_1 $和$ u_2 $，当时可以使用$ u_1 $ $ n_1 $ times，而$ u_2 $可以使用$ n_2 $ $ n_2 $ for $ n_2 $ n_2 \ n_2 \ ge ge（d-d-1 $ d-1 $ d-1 $）n_1 $。这些最佳策略是通过统一渠道的并行用途实现的，即使考虑了量子电路模型可实施的所有顺序和自适应策略。当固定统一通道的较小用途$ n_1 $的较小用途时，可以通过添加$ u_2 $的用途而不是$ n_2 =（d-1）n_1 $来提高最佳平均成功概率。此功能与纯状态比较的情况相反，在纯状态比较的情况下，添加更多未知纯状态的副本始终提高最佳平均成功概率。它突出显示了状态和通道的相应任务之间的区别，该任务先前已显示用于量子歧视任务。
Comparison of quantum objects is a task to determine whether two unknown quantum objects are the same or different. It is one of the most basic information processing tasks for learning property of quantum objects, and comparison of quantum states, quantum channels, and quantum measurements have been investigated. In general, repeated uses of quantum objects improve the success probability of comparison. The optimal strategy of pure-state comparison, the comparison of quantum states for the case of multiple copies of each unknown pure state, is known, but the optimal strategy of unitary comparison, the comparison of quantum channels for the case of multiple uses of each unknown unitary channel, was not known due to the complication of the varieties of causal order structures among the uses of each unitary channel. In this paper, we investigate unitary comparison with multiple uses of unitary channels based on the quantum tester formalism. We obtain the optimal minimum-error and the optimal unambiguous strategies of unitary comparison of two unknown $d$-dimensional unitary channels $U_1$ and $U_2$ when $U_1$ can be used $N_1$ times and $U_2$ can be used $N_2$ times for $N_2 \ge (d-1)N_1$. These optimal strategies are implemented by parallel uses of the unitary channels, even though all sequential and adaptive strategies implementable by the quantum circuit model are considered. When the number of the smaller uses of the unitary channels $N_1$ is fixed, the optimal averaged success probability cannot be improved by adding more uses of $U_2$ than $N_2 = (d-1) N_1$. This feature is in contrast to the case of pure-state comparison, where adding more copies of the unknown pure states always improves the optimal averaged success probability. It highlights the difference between corresponding tasks for states and channels, which has been previously shown for quantum discrimination tasks.
