Quantum advantages for Pauli channel estimation

We show that entangled measurements provide an exponential advantage in sample complexity for Pauli channel estimation, which is both a fundamental problem and practically important subroutine benchmarking near-term quantum devices. The specific task we consider to simultaneously learn all the eigenvalues of $n$-qubit $\pm\varepsilon$ precision. give estimation protocol with ancilla succeeds high probability using only $O(n/\varepsilon^{2})$ copies channel, while prove any ancilla-free (possibly adaptive control concatenation) would need at least $\Omega(2^{n/3})$ rounds measurement. further study advantages provided by small number ancillas. For case $k$-qubit ($k\le n$) available, obtain lower bound $\Omega(2^{(n-k)/3})$ non-concatenating protocol, stronger $\Omega(n2^{n-k})$ non-adaptive, shown be tight. also how apply ancilla-assisted practical noise-resilient sample-efficient manner, given reasonable noise assumptions. Our results practically-interesting example learning bring new insight benchmarking.