论文标题
设计随机通道
Designing Stochastic Channels
论文作者
论文摘要
随机通道在量子信息领域无处不在，因为它们简单易于分析。特别是，Pauli通道和去极化通道进行了广泛的研究，因为它们可以在许多相关的量子电路中有效模拟。尽管它们广泛使用，但一般随机通道的特性很少受到关注。在本文中，我们证明了一般随机通道的钻石距离与身份相吻合的钻石距离与该身份的过程不相关。我们以一个明确的例子证明，存在非统一的多数随机通道。然后，我们讨论统一的1-Designs和随机通道之间的关系。我们证明，统一的1个设计始终是随机通道的任意量子通道的旋转。但是，与统一的2设计不同，旋转的通道取决于单位1设计的选择。此外，我们以例如例子证明，存在随机通道，这些通道无法通过通过单位的1-Design旋转量子通道来获得。
Stochastic channels are ubiquitous in the field of quantum information because they are simple and easy to analyze. In particular, Pauli channels and depolarizing channels are widely studied because they can be efficiently simulated in many relevant quantum circuits. Despite their wide use, the properties of general stochastic channels have received little attention. In this paper, we prove that the diamond distance of a general stochastic channel from the identity coincides with its process infidelity to the identity. We demonstrate with an explicit example that there exist multi-qubit stochastic channels that are not unital. We then discuss the relationship between unitary 1-designs and stochastic channels. We prove that the twirl of an arbitrary quantum channel by a unitary 1-design is always a stochastic channel. However, unlike with unitary 2-designs, the twirled channel depends upon the choice of unitary 1-design. Moreover, we prove by example that there exist stochastic channels that cannot be obtained by twirling a quantum channel by a unitary 1-design.
