2020
DOI: 10.48550/arxiv.2009.00632
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Microstate Distinguishability, Quantum Complexity, and the Eigenstate Thermalization Hypothesis

Ning Bao,
Jason Pollack,
David Wakeham
et al.

Abstract: In this work, we use quantum complexity theory to quantify the difficulty of distinguishing eigenstates obeying the Eigenstate Thermalization Hypothesis (ETH). After identifying simple operators with an algebra of low-energy observables and tracing out the complementary high-energy Hilbert space, the ETH leads to an exponential suppression of trace distance between the coarse-grained eigenstates. Conversely, we show that an exponential hardness of distinguishing between states implies ETH-like matrix elements.… Show more

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