AI 中文总结
研究针对酉和反酉对称下的破对称投影测量及酉门，基于双目标无编程不等式建立定量维格纳-荒木-柳濑型定理，将测量或门误差转化为设备状态不对称下限，为对称受限量子测量和控制提供基本限制。
AI 中文摘要
对称性对量子测量和控制施加了基本限制。维格纳-荒木-柳濑定理及其定量扩展从守恒生成元的涨落方面捕捉了连续对称性的这种限制。然而，这种基于生成元的界限并未为离散酉对称性或反酉对称性提供定量限制。在此，我们针对任意酉和反酉对称下的破对称投影测量和酉门建立了定量的维格纳-荒木-柳濑型定理。我们的方法基于一个双目标无编程不等式：如果单个处理器近似实现两个放大可区分性的操作，那么相应的程序状态本身必须是可区分的。应用于对称实现时，这将非对称测量或门的误差直接转换为设备状态不对称性的下限，通过其与对称变换副本的保真度来量化。我们的结果适用于离散和反酉对称，从而为超出连续对称范围的对称受限量子测量和控制提供了一个基本限制。
英文摘要
Symmetry imposes fundamental constraints on quantum measurement and control. The Wigner-Araki-Yanase theorem and its quantitative extensions capture this restriction for continuous symmetries, in terms of fluctuations of conserved generators. Such generator-based bounds, however, do not provide quantitative limitations for discrete unitary symmetries or for antiunitary symmetries. Here we establish quantitative WAY-type theorems for symmetry-breaking projective measurements and unitary gates under arbitrary unitary and antiunitary symmetries. Our approach is based on a two-target no-programming inequality: if a single processor approximately implements two operations that amplify distinguishability, then the corresponding program states must themselves be distinguishable. Applied to symmetric implementations, this converts the error of an asymmetric measurement or gate directly into a lower bound on the asymmetry of the apparatus state, quantified by its fidelity with its symmetry-transformed copy. Our results apply to discrete and antiunitary symmetries, thereby providing a fundamental limit for symmetry-limited quantum measurement and control beyond the continuous-symmetry regime.
Comments8+4pages, 2 figures
