Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Microstate Distinguishability, Quantum Complexity, and the Eigenstate
  Thermalization Hypothesis   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.

21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph