Full time-dependent counting statistics of highly entangled biphoton states

TL;DR

This paper introduces an efficient method for calculating the full time-dependent counting statistics of highly entangled biphoton states, accounting for spatial modes and various interaction times, with applications in quantum communication security.

Contribution

It provides a novel, versatile approach for predicting biphoton detection statistics over time, including accidental correlations and effects of optical components.

Findings

Valid for a wide range of entanglement and interaction times

Classifies time intervals to analyze correlations and accidental events

Estimates detuning ranges to ensure quantum key security

Abstract

Highly entangled biphoton states, generated by spontaneous parametric processes, find wide applications in many experimental realizations. There is an increasing demand for accurate prediction of their time-dependent detection. Unlike approaches that have emerged so far, this paper presents an approach providing full time-dependent counting statistics in terms of efficiently computable formulas, valid for a wide range of entanglement and arbitrary interaction times. General spatial modes are taken into account to describe free space and fiber propagation. The time intervals that correspond to the statistics are classified according to their widths. Apart from large and small widths compared to the temporal correlation width, intermediate interval widths give access to accidental correlations between separated time intervals. Moreover, the approach is easily applicable to a modular array of arbitrary optical components and external influences. This is demonstrated on phase-time coding, where the detuning of the interferometers affecting Franson interference is investigated. An acceptable range for the detuning is estimated, such that the security of the key is not compromised.