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Measurement with indefinite causal order and the Sagnac interferometer.

S M Barnett1, S Croke1, S Franke-Arnold1

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Summary
This summary is machine-generated.

Indefinite causal order measurements, realized in a Sagnac interferometer, can measure the Pancharatnam-Berry phase. This quantum optics approach extends to arbitrary quantum states of light.

Keywords:
Sagnac interferometer

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Area of Science:

  • Quantum optics
  • Quantum information science
  • Interferometry

Background:

  • Indefinite causal order offers advantages over fixed-order operations.
  • Sagnac interferometers naturally implement these indefinite causal orders in optical systems.

Purpose of the Study:

  • To demonstrate that a Sagnac interferometer can measure the Pancharatnam-Berry phase.
  • To extend the analysis to a fully quantized treatment for arbitrary quantum states of light.

Main Methods:

  • Utilizing a Sagnac interferometer to realize indefinite causal order.
  • Applying unitary transformations to the polarization of light.
  • Extending from classical/single-photon to a fully quantized treatment.

Main Results:

  • The Sagnac interferometer setup measures the solid angle enclosed by unitary transformations on the Poincaré sphere.
  • This measurement corresponds to the Pancharatnam-Berry phase.
  • The quantized treatment allows analysis for arbitrary quantum states of light.

Conclusions:

  • Sagnac interferometers are effective tools for measuring the Pancharatnam-Berry phase in quantum optics.
  • The study provides a foundation for analyzing quantum states using indefinite causal order in optical experiments.