论文标题
Wigner-Araki-yanase定理，用于连续和无限的可观察物
Wigner-Araki-Yanase theorem for continuous and unbounded conserved observables
论文作者
论文摘要
Wigner-araki-yanase（方式）定理指出，加性保护法暗示着可以实现的投影测量和系统的保守可观察到的可观察到的合理性。该定理的已知证明仅限于系统的有界或离散光谱的可观察物，并且不适用于动量操作员等无界和连续可观察的物品。在这封信中，我们介绍了在Yanase条件下可能无界且连续的可观察物的定理的方式，该方式要求探针正算子值措施应与可观察到的探针系统的保守量相上的通勤。由于这种方式定理，我们表明，使用线性光学仪器和光子计数器在动量保护下的投射测量和正交振幅的射击测量的精确实现是不可能的。我们还考虑了根据保护法的实现单一渠道的实施，发现如果$ l_s $是半构建的，则可以使用实施的单一$ u_s $通勤的可观察到的$ L_S $通勤，而$ u_s^\ dagger l_s u_s $如果$ l_s $ spectrum spectrum and down-n-d offer-l_s $ speptrum and down-n-d offer-n nofd and down-splowed and down and down-ninf oss uncned and down-splowed and down and down-ninf oss uncned and。我们提供了后一种情况的简单示例，其中$ l_s $是动量操作员。
The Wigner-Araki-Yanase (WAY) theorem states that additive conservation laws imply the commutativity of exactly implementable projective measurements and the conserved observables of the system. Known proofs of this theorem are only restricted to bounded or discrete-spectrum conserved observables of the system and are not applicable to unbounded and continuous observables like a momentum operator. In this Letter, we present the WAY theorem for possibly unbounded and continuous conserved observables under the Yanase condition, which requires that the probe positive operator-valued measure should commute with the conserved observable of the probe system. As a result of this WAY theorem, we show that exact implementations of the projective measurement of the position under momentum conservation and of the quadrature amplitude using linear optical instruments and photon counters are impossible. We also consider implementations of unitary channels under conservation laws and find that the conserved observable $L_S$ of the system commute with the implemented unitary $U_S$ if $L_S$ is semi-bounded, while $U_S^\dagger L_S U_S$ can shift up to possibly non-zero constant factor if the spectrum of $L_S$ is upper and lower unbounded. We give simple examples of the latter case, where $L_S$ is a momentum operator.
