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Bulletin of the American Physical Society

Continuous Measurement Quantum State Reconstruction in an Almost Decoherence-Free Protocol

Carlos A. Riofrío, Seth Merkel, Ivan Deutsch

Published May 30, 2008• 0 citations
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We investigate the generation of uniform quantum state ensembles via continuous measurement. Using the SU(d)SU(d)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.