Nonstabilizerness determining the hardness of direct fidelity estimation

In this work, we show how the resource theory of nonstabilizerness quantifies hardness direct fidelity estimation protocols. particular, resources needed for a conducted on generic states, such as Pauli and shadow protocols, grow exponentially with stabilizer R\'enyi entropy. Remarkably, these protocols are shown to be feasible only those states that useless attain any quantum speedup or advantage. This result suggests impossibility estimating efficiently and, at same time, leaves window open specialized directly particular states. We then extend our results evolutions, showing certify quality implementation given unitary $U$ governed by in Choi state associated $U$, which is possess profound connection out-of-time order correlators.