Measurement with indefinite causal order and the Sagnac interferometer

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.