Time-symmetric quantum theory of smoothing

Area of Science:

• Quantum physics
• Quantum information science
• Estimation theory

Background:

• Smoothing is an estimation technique utilizing past and future observations for enhanced accuracy over filtering alone.
• Prior work exists on classical and quantum filtering, retrodiction, and smoothing.

Purpose of the Study:

• To construct a quantum theory of smoothing.
• To generalize prior work on classical and quantum estimation techniques.
• To address the problem of optimally estimating classical Markov processes coupled to quantum systems under continuous measurements.

Main Methods:

• Development of a time-symmetric formalism for quantum smoothing.
• Generalization of existing classical and quantum filtering and smoothing theories.

Main Results:

• A novel quantum theory of smoothing has been constructed.
• The theory optimally estimates classical Markov processes coupled to quantum systems under continuous measurements.

Conclusions:

• The developed quantum smoothing theory offers a significant advancement in estimation techniques.
• Expected to have major applications in quantum sensing systems like gravitational wave detectors and atomic magnetometers.