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Quantum State Smoothing.

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We introduce a smoothed quantum state for partially monitored quantum systems, using all available past and future observations. This method enhances state estimation compared to traditional filtering techniques.

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Area of Science:

  • Quantum mechanics
  • Quantum information theory
  • Statistical estimation

Background:

  • Classical smoothing conditions probability distributions on all-time observations.
  • Partially monitored open quantum systems lack complete measurement data.
  • Quantum trajectories conventionally rely on past observations (filtering).

Purpose of the Study:

  • To define and calculate a smoothed quantum state for partially monitored open quantum systems.
  • To investigate the impact of unobserved data on quantum state estimation.
  • To compare the purity of smoothed states with conventionally filtered states.

Main Methods:

  • Defining a smoothed quantum state conditioned on an all-time monitoring record.
  • Calculating the smoothed distribution for a hypothetical complete record.
  • Averaging pure states over the smoothed distribution to obtain the mixed smoothed state.

Main Results:

  • The smoothed quantum state is conditioned on both past and future observations.
  • A hypothetical unobserved record is used to complete the monitoring.
  • The choice of unraveling affects the purity increase of the smoothed state.

Conclusions:

  • Smoothed quantum states provide a more refined estimation for partially monitored systems.
  • This approach offers a potential improvement over conventional quantum state filtering.
  • The study highlights the influence of unraveling on state purity in quantum estimation.