Purification of weakly monitored Clifford circuits on prime-dimensional qudits reduces exactly to a pure-death Markov process on the density-matrix rank, producing compact universal scaling functions for all Rényi entropies.
Elusive phase transition in the replica limit of monitored systems
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abstract
We study an exactly solvable model of monitored dynamics in a system of $N$ spin-$1/2$ particles with pairwise all-to-all noisy interactions, where each spin is continuously weakly measured along a random direction. Using the replica trick to incorporate the Born-rule weighting of measurement outcomes, we obtain an exact large-$N$ description of purification and of the statistics of local observables. We find that the nature of the phase transition strongly depends on the number $n$ of replicas: non-perturbative logarithmic corrections appear in the physically relevant $n\to1$ limit and destroy the purifying phase present at finite integer $n$. As a consequence, the purification time of an initially mixed state is always exponentially long in the system size, even at arbitrarily large measurement rate.
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quant-ph 3representative citing papers
A most-likely-trajectory method exactly solves Gaussian bosonic monitoring and approximates the Sine-Gordon model to show an entanglement phase transition from area-law to logarithmic scaling.
Measurement-based quantum diffusion models are introduced to recover pure and mixed quantum states via weak measurements, quantum score matching, and Petz recovery maps with error bounds, bridging to classical stochastic reversals.
citing papers explorer
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Universal purification dynamics of monitored Clifford circuits
Purification of weakly monitored Clifford circuits on prime-dimensional qudits reduces exactly to a pure-death Markov process on the density-matrix rank, producing compact universal scaling functions for all Rényi entropies.
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Measurement-induced phase transition in interacting bosons from most likely quantum trajectory
A most-likely-trajectory method exactly solves Gaussian bosonic monitoring and approximates the Sine-Gordon model to show an entanglement phase transition from area-law to logarithmic scaling.
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Measurement-Based Quantum Diffusion Models
Measurement-based quantum diffusion models are introduced to recover pure and mixed quantum states via weak measurements, quantum score matching, and Petz recovery maps with error bounds, bridging to classical stochastic reversals.