Decoding the Entanglement Structure of Monitored Quantum Circuits
- URL: http://arxiv.org/abs/2109.08691v1
- Date: Fri, 17 Sep 2021 18:00:00 GMT
- Title: Decoding the Entanglement Structure of Monitored Quantum Circuits
- Authors: Beni Yoshida
- Abstract summary: We find that the entanglement structure of a monitored quantum circuit in the volume-law phase is largely independent of the initial states.
We derive a general relation between the code distance and the sub-leading contribution to the volume-law entanglement entropy.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Given an output wavefunction of a monitored quantum circuit consisting of
both unitary gates and projective measurements, we ask whether two
complementary subsystems are entangled or not. For Clifford circuits, we find
that this question can be mapped to a certain classical error-correction
problem where various entanglement measures can be explicitly computed from the
recoverability. The dual classical code is constructed from spacetime patterns
of out-of-time ordered correlation functions among local operators and measured
Pauli operators in the past, suggesting that the volume-law entanglement in a
monitored circuit emerges from quantum information scrambling, namely the
growth of local operators. We also present a method of verifying quantum
entanglement by providing a simple deterministic entanglement distillation
algorithm, which can be interpreted as decoding of the dual classical code.
Discussions on coding properties of a monitored Clifford circuit, including
explicit constructions of logical and stabilizer operators, are also presented.
Applications of our framework to various physical questions, including
non-Clifford systems, are discussed as well. Namely, we argue that the
entanglement structure of a monitored quantum circuit in the volume-law phase
is largely independent of the initial states and past measurement outcomes
except recent ones, due to the decoupling phenomena from scrambling dynamics,
up to a certain polynomial length scale which can be identified as the code
distance of the circuit. We also derive a general relation between the code
distance and the sub-leading contribution to the volume-law entanglement
entropy. Applications of these results to black hole physics are discussed as
well.
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