Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Measurement-Driven Phase Transition within a Volume-Law Entangled Phase   We identify a phase transition between two kinds of volume-law entangled
phases in non-local but few-body unitary dynamics with local projective
measurements. In one phase, a finite fraction of the system belongs to a
fully-entangled state, one for which no subsystem is in a pure state, while in
the second phase, the steady-state is a product state over extensively many,
finite subsystems. We study this "separability" transition in a family of
solvable models in which we analytically determine the transition point, the
evolution of certain entanglement properties of interest, and relate this to a
mean-field percolation transition. Since the entanglement entropy density does
not distinguish these phases, we introduce the entangling power - which
measures whether local measurements outside of two finite subsystems can boost
their mutual information - as an order parameter, after considering its
behavior in tensor network states, and numerically studying its behavior in a
model of Clifford dynamics with measurements. We argue that in our models, the
separability transition coincides with a transition in the computational
"hardness" of classically determining the output probability distribution for
the steady-state in a certain basis of product states. A prediction for this
distribution, which is accurate in the separable phase, and should deviate from
the true distribution in the fully-entangled phase, provides a possible
benchmarking task for quantum computers.

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The categories of this paper are: q-fin
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio