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arXiv · 2606.31848

Generating uniform quantum state ensembles with continuous measurement

Theodore McKeever·Ahsan Nazir·Harry J. D. Miller
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Abstract

We investigate the generation of uniform quantum state ensembles via continuous measurement. Using the $SU(d)$ Bloch representation, we derive the associated Langevin and Fokker-Planck equations and identify geometric conditions under which homogeneous monitoring causes global convergence to the uniform pure-state ensemble. We then extend the analysis to mixed states, showing that homogeneous purity-dependent decoherence rates generate uniform Hilbert-Schmidt and Bures ensembles of qubit states through an effective nonlinear stochastic evolution. Additionally, we introduce a post-mixing protocol for qubits: target mixed-state ensembles are assembled by classically sampling trajectories generated with different fixed efficiencies (or decoherence rates). This provides an experimentally feasible route to reconstructing Hilbert-Schmidt and Bures-random mixed-state ensembles, demonstrating that continuous monitoring provides both an exact dynamical generator of Haar-random pure states and a practical route to constructing mixed-state ensembles.

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Theodore McKeever, Ahsan Nazir, Harry J. D. Miller. 2026-06-30. Generating uniform quantum state ensembles with continuous measurement. https://arxiv.org/abs/2606.31848

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