Microstate distinguishability, quantum complexity, and the eigenstate thermalization hypothesis. (15th July 2021)

• Record Type: Journal Article
• Authors: Bao, Ning; Pollack, Jason; Wakeham, David; Wildenhain, Elizabeth
• Is Part Of: Classical and quantum gravity. Volume 38:Number 15(2021)
• Publication Date: 2021-07-15
• Subjects: eigenstate thermalization hypothesis -- coarse-graining -- quantum complexity; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/1361-6382/ac0e17
• Languages: English
• ISSNs: 0264-9381

Abstract

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. The BBBV lower bound on the query complexity of Grover search then translates directly into a complexity-theoretic statement lower bounding the hardness of distinguishing these reduced states.