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<p>We show that, in long-time, quantum trajectories select an invariant subspace of the Hilbert space of the system being indirectly measured. This selection is shown to be exponentially fast in an almost sure sense and in average. Moreover, the selection mimics a unique positive operator measurement. This generalizes known results for non-demolition measurements to arbitrary repeated indirect measurements.</p>

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Exponentially Fast Selection of Sectors for Quantum Trajectories Beyond Non-demolition Measurements

  • 期刊论文

  • 发表日期：

    2025年11月23日

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  • Tristan Benoist,
  • Linda Greggio,
  • Clément Pellegrini

摘要

We show that, in long-time, quantum trajectories select an invariant subspace of the Hilbert space of the system being indirectly measured. This selection is shown to be exponentially fast in an almost sure sense and in average. Moreover, the selection mimics a unique positive operator measurement. This generalizes known results for non-demolition measurements to arbitrary repeated indirect measurements.