Understand
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.