“…Metrology, which studies the precision limit of measurement and estimation, plays a central role in science and technology. Recently quantum metrology, which exploits quantum mechanical effects to achieve far better precision than classical schemes , has gained increasing attention and has found wide applications in various fields, such as gravitational wavedetection [19,[23][24][25][26][27], quantum phase estimation [5,[28][29][30][31], quantum magnetometer [32,33], quantum ranging [34][35][36], quantum spectroscopy [37][38][39][40], quantum imaging [41][42][43][44][45][46][47], quantum target-detection [48,49], quantum gyroscope [50,51], distributed quantum sensing [52][53][54], atomic clocksynchronization [55][56][57][58][59][60][61], and even biological measurements [62].…”