Inferring physical properties of symmetric states from the fewest copies

TL;DR

This paper introduces an entangled measurement strategy leveraging symmetric structures of states to significantly reduce the number of samples needed for inferring physical properties of high-dimensional quantum states, with proven optimality and practical applicability.

Contribution

It proposes a novel symmetrization-based measurement method that drastically lowers sample complexity in quantum state property inference, improving efficiency over existing techniques.

Findings

Achieves exponential reduction in sample complexity in various experimental scenarios

Proven to be optimal under natural assumptions

Easily integrable into existing quantum measurement frameworks

Abstract

Learning physical properties of high-dimensional states is crucial for developing quantum technologies but usually consumes an exceedingly large number of samples which are difficult to afford in practice. In this Letter, we use the methodology of quantum metrology to tackle this difficulty, proposing a strategy built upon entangled measurements for dramatically reducing sample complexity. The strategy, whose characteristic feature is symmetrization of observables, is powered by the exploration of symmetric structures of states which are ubiquitous in physics. It is provably optimal under some natural assumption, efficiently implementable in a variety of contexts, and capable of being incorporated into existing methods as a basic building block. We apply the strategy to different scenarios motivated by experiments, demonstrating exponential reductions in sample complexity.