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Area of Science:

  • Quantum Optics
  • Quantum Information Theory
  • Quantum Measurement

Background:

  • Traditional Stokes operators are essential for describing polarization states in classical and quantum optics.
  • Bell inequalities are crucial for testing local realism and demonstrating quantum entanglement.
  • Squeezed vacuum states are non-classical states of light with applications in quantum technologies.

Purpose of the Study:

  • To introduce a simplified form of Stokes operators for quantum optical fields.
  • To explore the utility of these simplified operators in Bell-type measurements.
  • To investigate their effectiveness for states with an undefined photon number, such as squeezed vacuum states.

Main Methods:

  • Development of simplified Stokes operators based on photon number measurements and a binning procedure.
  • Application of these operators in Bell-type measurements using polarization analyzers.
  • Numerical simulations to test violations of Bell inequalities for four-mode squeezed vacuum states.

Main Results:

  • The simplified observables, while not possessing all properties of standard Stokes operators, are suitable for Bell measurements.
  • These observables demonstrate robust violations of associated Bell inequalities.
  • Numerical evidence suggests violations of local realism for four-mode squeezed vacuum states across all pumping powers.

Conclusions:

  • The proposed simplified Stokes operators provide an intuitive and effective tool for Bell-type measurements, particularly for non-classical states.
  • These observables facilitate robust demonstrations of quantum correlations and violations of local realism.
  • The findings open avenues for experimental verification of quantum phenomena using readily implementable techniques.