Inferring physical properties of symmetric states from the fewest copies

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.

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Cited by in corpus (8)

• Review: Quantum Metrology and Sensing with Many-Body Systems
• Krylov shadow tomography: Efficient estimation of quantum Fisher information
• Maximal Steered Coherence in Accelerating Unruh-DeWitt Detectors
• Symmetric quantum states: a review of recent progress
• Retrieving maximum information of symmetric states from their corrupted copies
• Superiority of Krylov shadow tomography in estimating quantum Fisher information: From bounds to exactness
• Measuring Incompatible Observables with Quantum Neural Networks
• Scalable protocol to coherence estimation from scarce data: Theory and experiment