Frequency-Resolved Simulations of Highly Entangled Biphoton States: Beyond the Single-Pair Approximation. I. Theory

TL;DR

This paper introduces a spectral amplitude expansion method for simulating highly entangled biphoton states, surpassing traditional single-pair approximations by accurately capturing multi-pair correlations.

Contribution

It presents a novel expansion approach that efficiently models multi-pair spectral correlations in highly entangled biphoton states, improving simulation accuracy.

Findings

The expansion accurately models highly entangled states beyond single-pair approximations.

The lowest order corresponds to the infinitely entangled limit with uncorrelated pairs.

Higher orders incorporate correlations between different photon pairs.

Abstract

We discuss an expansion of the detection probabilities of biphoton states in terms of increasing orders of the joint spectral amplitude. The expansion enables efficient time- or frequency-resolved numerical simulations involving quantum states exhibiting a high degree of spectral entanglement. Contrary to usual approaches based on one- or two-pair approximations, we expand the expressions in terms corresponding to the amount of correlations between different pairs. The lowest expansion order corresponds to the limit of infinitely entangled states, where different pairs are completely uncorrelated and the full multi-pair statistics are inferred from a single pair. We show that even this limiting case always yields more accurate results than the single-pair approximation. Higher expansion orders describe deviations from the infinitely entangled case and introduce correlations between the photons of different pairs.