Equivalently, one fewer replica necessarily places the problem in a dimension-growing lower-bound regime, while⌈t/2⌉replicas already reach the known attainable regime

Since the upper-bound side is already known at⌈t/2⌉ replicas [3], this pins the exact replica threshold for estimating tr(ρt) at t 2

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quant-ph · 2026-04-24 · unverdicted · novelty 7.0

Exact replica threshold for tr(ρ^t) is ⌈t/2⌉, with fewer replicas incurring dimension-dependent sample complexity.

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The Exact Replica Threshold for Nonlinear Moments of Quantum States quant-ph · 2026-04-24 · unverdicted · none · ref 1
Exact replica threshold for tr(ρ^t) is ⌈t/2⌉, with fewer replicas incurring dimension-dependent sample complexity.