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Microstate distinguishability, quantum complexity, and the eigenstate thermalization hypothesis
- Source :
- Classical and Quantum Gravity. 38:154004
- Publication Year :
- 2021
- Publisher :
- IOP Publishing, 2021.
-
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.<br />19 pages, 4 figures; minor changes
- Subjects :
- High Energy Physics - Theory
Physics
Quantum Physics
Physics and Astronomy (miscellaneous)
Hilbert space
FOS: Physical sciences
Observable
Microstate (statistical mechanics)
symbols.namesake
High Energy Physics - Theory (hep-th)
symbols
Trace distance
Statistical physics
Quantum Physics (quant-ph)
Quantum
Eigenstate thermalization hypothesis
Eigenvalues and eigenvectors
Quantum complexity theory
Subjects
Details
- ISSN :
- 13616382 and 02649381
- Volume :
- 38
- Database :
- OpenAIRE
- Journal :
- Classical and Quantum Gravity
- Accession number :
- edsair.doi.dedup.....b694168c9bae16976a1dfb014aae2c4f