Continuous monitoring with jump operators forming a deformed unitary 1-design rigorously produces the Scrooge ensemble as the unique late-time equilibrium distribution of quantum trajectories for any target density matrix.
The Scrooge ensemble in many-body quan- tum systems
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Low-energy states of local Hamiltonians have half-system entanglement entropies upper-bounded by the thermal entropies of two fictitious systems whose combined energies match the state's energy.
For single-logical-qubit surface codes with uniform X rotations, the projected logical ensemble after syndrome extraction and maximum-likelihood decoding is isomorphic to scattering-matrix ensembles of chaotic quantum dots in Altland-Zirnbauer classes D or DIII.
Quantum resource theories split into smoothly localizable (continuous local resource change) and threshold localizable (discontinuous jump past critical density) classes, driven by block sharpening, with predictions for phase boundaries validated numerically.
Absence of simple slow operators implies that typical low-complexity states thermalize in quantum systems.
The paper establishes that typical states in a grand-canonical micro-canonical Hilbert subspace produce the grand-canonical density matrix and a GAP/Scrooge wave-function distribution for the subsystem.
citing papers explorer
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Exact Hilbert-space ergodicity from continuous monitoring
Continuous monitoring with jump operators forming a deformed unitary 1-design rigorously produces the Scrooge ensemble as the unique late-time equilibrium distribution of quantum trajectories for any target density matrix.
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Quantum matter is weakly entangled at low energies
Low-energy states of local Hamiltonians have half-system entanglement entropies upper-bounded by the thermal entropies of two fictitious systems whose combined energies match the state's energy.
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Projected logical ensembles in surface codes via the random-matrix theory of quantum dots
For single-logical-qubit surface codes with uniform X rotations, the projected logical ensemble after syndrome extraction and maximum-likelihood decoding is isomorphic to scattering-matrix ensembles of chaotic quantum dots in Altland-Zirnbauer classes D or DIII.
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Quantum resource localizability transitions in deep thermalization
Quantum resource theories split into smoothly localizable (continuous local resource change) and threshold localizable (discontinuous jump past critical density) classes, driven by block sharpening, with predictions for phase boundaries validated numerically.
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Simple slow operators and quantum thermalization
Absence of simple slow operators implies that typical low-complexity states thermalize in quantum systems.
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Grand-Canonical Typicality
The paper establishes that typical states in a grand-canonical micro-canonical Hilbert subspace produce the grand-canonical density matrix and a GAP/Scrooge wave-function distribution for the subsystem.