Quantum Fisher information and photon statistics from shift current shot noise.

Photon-number fluctuations encoded in shift current shot noise reveal the photon-number variance, with the Fano factor proportional to this variance, enabling quantum optical measurements.

• Why it matters: Accurately measuring quantum optical statistics and quantum Fisher information is crucial for advancing high-precision phase measurements and understanding multiphoton entanglement, but converting photon fluctuations into electrical signals remains challenging.
• What they did: The authors theoretically predict that a photodetector utilizing the shot noise of the quantum-geometric shift current of exciton polaritons can measure photon-number statistics and infer QFI for pure states by solving the Lindblad equation for arbitrary initial photon states.
• The result: The integrated current depends solely on the mean photon number, while the shot noise's Fano factor relates directly to photon-number variance, confirmed numerically for optical Schrödinger cat and squeezed-vacuum states, enabling high-precision quantum measurements in solid-state platforms.