论文标题
量子测量和散射类型的操作的局限性在节能定律下
Limitations of Quantum Measurements and Operations of Scattering Type under the Energy Conservation Law
论文作者
论文摘要
提高工程和基本物理学中量子测量和操作的准确性非常重要。然而，众所周知，根据Wigner-Araki-yanase定理（定理）及其概括，测量和单一操作的可实现准确性通常受到保护法的限制。尽管许多研究已经按定量定理扩展了方式，但它们中的大多数以及定理的原始方法都涉及诸如角度动量保护法之类的添加剂保护法。在本文中，我们探讨了能源保护法所产生的局限性，该法律是普遍的，但这是非加性保护法之一。我们使用满足能量保护定律的散射过程，为量子测量的误差提供了下限。我们获得了控制系统必须实现的条件，以便在考虑散射过程时实现具有零误差的受控统一门。我们还显示了受控统一门的栅极保真度的上限与系统的能量波动之间的定量关系，而目标系统和控制系统都是一个量子。
It is important to improve the accuracy of quantum measurements and operations both in engineering and fundamental physics. It is known, however, that the achievable accuracy of measurements and unitary operations are generally limited by conservation laws according to the Wigner-Araki-Yanase theorem (WAY theorem) and its generalizations. Although many researches have extended the WAY theorem quantitatively, most of them, as well as the original WAY theorem, concern only additive conservation laws like the angular momentum conservation law. In this paper, we explore the limitation incurred by the energy conservation law, which is universal but is one of the non-additive conservation laws. We present a lower bound for the error of a quantum measurement using a scattering process satisfying the energy conservation law. We obtain conditions that a control system Hamiltonian must fulfill in order to implement a controlled unitary gate with zero error when a scattering process is considered. We also show the quantitative relationship between the upper bound of the gate fidelity of a controlled unitary gate and the energy fluctuation of systems when a target system and a control system are both one qubit.
