Rigorous calibration method for photon-number statistics

TL;DR

This paper introduces a rigorous calibration method for photon-number statistics using a Hanbury-Brown-Twiss setup, providing quantitative bounds essential for quantum information applications like quantum cryptography.

Contribution

It develops a general framework for photon-number calibration with multiple detectors, offering closed-form bounds and demonstrating optimality for low photon numbers.

Findings

Provides rigorous bounds on photon-number distributions

Applicable to quantum cryptography protocols like decoy-state QKD

Achieves near-optimal secure key rates with four detectors

Abstract

Characterization of photon statistics of a light source is one of the most basic tools in quantum optics. Although the outcome from existing methods is believed to be a good approximation when the measured light is sufficiently weak, there is no rigorous quantitative bounds on the degree of the approximation. As a result, they fail to fulfill the demand arising from emerging applications of quantum information such as quantum cryptography. Here, we propose a calibration method to produce rigorous bounds for a photon-number probability distribution by using a conventional Hanbury-Brown-Twiss setup with threshold photon detectors. We present a general framework to treat any number of detectors and non-uniformity of their efficiencies. The bounds are conveniently given as closed-form expressions of the observed coincidence rates and the detector efficiencies. We also show optimality of the bounds for light with a small mean photon number. As an application, we show that our calibration method can be used for the light source in a decoy-state quantum key distribution protocol. It replaces the a priori assumption on the distribution that has been commonly used, and achieves almost the same secure key rate when four detectors are used for the calibration.