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Solvable Model of Quantum-Darwinism-Encoding Transitions.

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We introduce a solvable quantum Darwinism model demonstrating transitions in quantum information spread. This model shows distinct phases for information retrieval, with implications for understanding quantum information dynamics and measurement-induced phase transitions.

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Area of Science:

  • Quantum Information Science
  • Many-Body Quantum Systems
  • Quantum Dynamics

Background:

  • Quantum information spread in many-body systems under unitary dynamics is complex.
  • Understanding transitions in information encoding is crucial for quantum technologies.
  • Quantum Darwinism offers a framework for emergent classical objectivity.

Purpose of the Study:

  • To propose and analyze a solvable model of quantum Darwinism.
  • To investigate abrupt changes (transitions) in quantum information spreading.
  • To explore the relationship between quantum Darwinism and measurement-induced phase transitions (MIPTs).

Main Methods:

  • Utilized a random Clifford circuit on an expanding tree structure.
  • Entangled an input qubit with a reference qubit to track information.
  • Employed a two-replica calculation for comparison with exact results.

Main Results:

  • Identified a quantum Darwinism phase where information is retrievable from a small fraction of qubits.
  • Identified an encoding phase where such information retrieval is impossible.
  • Observed two continuous transitions separating these phases, with a mixed phase in between.

Conclusions:

  • The proposed model provides a tractable framework for studying quantum information encoding transitions.
  • The 'annealed' phase diagram from the replica calculation is robust and applies to Haar random unitaries.
  • A sharp MIPT is observed only with full environmental access in a modified eavesdropping model.