Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Subsystem Complexity and Holography   We study circuit complexity for spatial regions in holographic field
theories. We study analogues based on the entanglement wedge of the bulk
quantities appearing in the "complexity = volume" and "complexity = action"
conjectures. We calculate these quantities for one exterior region of an
eternal static neutral or charged black hole in general dimensions, dual to a
thermal state on one boundary with or without chemical potential respectively,
as well as for a shock wave geometry. We then define several analogues of
circuit complexity for mixed states, and use tensor networks to gain intuition
about them. We find a promising qualitative match between the holographic
action and what we call the purification complexity, the minimum number of
gates required to prepare an arbitrary purification of the given mixed state.
On the other hand, the holographic volume does not appear to match any of our
definitions of mixed-state complexity.

23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics