The Exact Replica Threshold for Nonlinear Moments of Quantum States

ArXi:2604.22627v1 Announce Type: cross Joint measurements on multiple copies of a quantum state provide access to nonlinear observables such as $\operatorname{tr}(\rho^t)$, but whether replica number marks a sharp information-theoretic resource boundary has remained unclear. For every fixed order $t\ge 3$, existing protocols show that $\lceil t/2\rceil$ replicas already suffice for polynomial-sample estimation of $\operatorname{tr}(\rho^t)$, yet it has remained open whether one fewer replica must necessarily incur a sample-complexity barrier growing with the dimension.