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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Partial projected ensembles from Haar-random states and scrambling circuits exhibit two information phases in Holevo information: exponential decay versus linear growth with system size, separated by sharp transitions and revealing a measurement-invisible quantum-correlated phase.
Measurement-induced entanglement in Tomonaga-Luttinger liquids is universal, conformally invariant, and arises from Born-rule averaging over conformally invariant boundary conditions in the CFT.
Continuous homogeneous monitoring generates Haar-uniform pure states and, via purity-dependent rates and post-mixing, uniform Hilbert-Schmidt and Bures mixed-state ensembles for qubits.
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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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Information phases of partial projected ensembles generated from random quantum states and scrambling dynamics
Partial projected ensembles from Haar-random states and scrambling circuits exhibit two information phases in Holevo information: exponential decay versus linear growth with system size, separated by sharp transitions and revealing a measurement-invisible quantum-correlated phase.
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Measurement-Induced Entanglement in Conformal Field Theory
Measurement-induced entanglement in Tomonaga-Luttinger liquids is universal, conformally invariant, and arises from Born-rule averaging over conformally invariant boundary conditions in the CFT.
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Generating uniform quantum state ensembles with continuous measurement
Continuous homogeneous monitoring generates Haar-uniform pure states and, via purity-dependent rates and post-mixing, uniform Hilbert-Schmidt and Bures mixed-state ensembles for qubits.