A Solvable Model of Quantum Darwinism-Encoding Transitions

Abstract

We propose a solvable model of Quantum Darwinism to encoding transitions -- abrupt changes in how quantum information spreads in a many-body system under unitary dynamics. We consider a random Clifford circuit on an expanding tree, whose input qubit is entangled with a reference. The model has a Quantum Darwinism phase, where one classical bit of information about the reference can be retrieved from an arbitrarily small fraction of the output qubits, and an encoding phase where such retrieval is impossible. The two phases are separated by a mixed phase and two continuous transitions. We compare the exact result to a two-replica calculation. The latter yields a similar ``annealed'' phase diagram, which applies also to a model with Haar random unitaries. We relate our approach to measurement induced phase transitions (MIPTs), by solving a modified model where an environment eavesdrops on an encoding system. It has a sharp MIPT only with full access to the environment.

18 pages, 6 figures; v2: expanded appendix, improved discussion

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Cited by in corpus (6)

• Fate of non-Hermitian free fermions with Wannier-Stark ladder
• Multipartite entanglement structure of monitored quantum circuits
• Dynamically generated concatenated codes and their phase diagrams
• Quantum Darwinism-encoding transitions on expanding trees
• Markovian to non-Markovian phase transition in the operator dynamics of a mobile impurity
• Metrological approach to the emergence of classical objectivity