Sublinear Copies Suffice for Fidelity Estimation with Pauli Measurements

2026-09-28

AI Summary

This study addresses the limitation in quantum state fidelity estimation where conventional measurement sample sizes scale linearly with system dimension, thereby restricting verification efficiency in high-dimensional scenarios. To overcome this challenge, the authors propose a sublinear sampling protocol based on Pauli-basis measurements combined with statistical inference algorithms, which transcends established cognitive constraints on traditional measurement lower bounds. Theoretically, this work demonstrates that high-dimensional quantum state fidelity estimation can be achieved with only o(d^0.9908/ε²) measurements for a given precision ε. By attaining sublinear sample complexity for the first time, the proposed approach significantly enhances the efficiency of quantum process verification.

Abstract

We present a protocol that estimates the quantum fidelity, up to precision $\varepsilon$, between a known target state and unknown lab-prepared state with sublinear, $o(d^{0.9908}/\varepsilon^2)$, number of Pauli basis measurements.

Problem

• Quantum fidelity estimation
• Pauli measurements
• Target state
• Unknown state

Innovation

• Quantum fidelity estimation
• Pauli measurements
• Sublinear complexity
• Quantum state tomography