Measurement-induced phase transitions on dynamical quantum trees
- URL: http://arxiv.org/abs/2210.07264v2
- Date: Mon, 11 Sep 2023 21:17:25 GMT
- Title: Measurement-induced phase transitions on dynamical quantum trees
- Authors: Xiaozhou Feng, Brian Skinner, and Adam Nahum
- Abstract summary: We show a transition at a nontrivial value of the measurement strength, with the real measurement case exhibiting a smaller entangling phase.
An intriguing difference between the two cases is that the real measurement case lies at the boundary between two distinct types of critical scaling.
We propose a protocol for realizing a measurement phase transition experimentally via an expansion process.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Monitored many-body systems fall broadly into two dynamical phases,
``entangling'' or ``disentangling'', separated by a transition as a function of
the rate at which measurements are made on the system. Producing an analytical
theory of this measurement-induced transition is an outstanding challenge.
Recent work made progress in the context of tree tensor networks, which can be
related to all-to-all quantum circuit dynamics with forced (postselected)
measurement outcomes. So far, however, there are no exact solutions for
dynamics of spin-1/2 degrees of freedom (qubits) with ``real'' measurements,
whose outcome probabilities are sampled according to the Born rule. Here we
define dynamical processes for qubits, with real measurements, that have a
tree-like spacetime interaction graph, either collapsing or expanding the
system as a function of time. The former case yields an exactly solvable
measurement transition. We explore these processes analytically and
numerically, exploiting the recursive structure of the tree. We compare the
case of ``real'' measurements with the case of ``forced'' measurements. Both
cases show a transition at a nontrivial value of the measurement strength, with
the real measurement case exhibiting a smaller entangling phase. Both exhibit
exponential scaling of the entanglement near the transition, but they differ in
the value of a critical exponent. An intriguing difference between the two
cases is that the real measurement case lies at the boundary between two
distinct types of critical scaling. On the basis of our results we propose a
protocol for realizing a measurement phase transition experimentally via an
expansion process.
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