Characterizing entanglement in pulsed parametric downconversion using chronocyclic Wigner functions

TL;DR

This paper explores the spectral-temporal entanglement in pulsed parametric downconversion by analyzing the four-dimensional chronocyclic Wigner function, providing a new way to measure and understand entanglement in quantum photon pairs.

Contribution

It introduces a novel approach using the chronocyclic Wigner function to characterize entanglement in pulsed PDC states, linking discrete and continuous variable descriptions.

Findings

Conditioned time-bandwidth product as an entanglement measure

Demonstrates versatility across various PDC conditions

Highlights link between discrete and continuous variable frameworks

Abstract

Pulsed parametric downconversion (PDC) processes generate photon pairs with a rich spectral-temporal structure, which offer an attractive potential for quantum information and communication applications. In this paper, we investigate the four-dimensional chronocyclic Wigner function of the PDC state, which naturally lends itself to the pulsed characteristics of these states. From this function we derive the conditioned time-bandwidth product of one of the pair photons, a quantity which is not only a valid measure of entanglement between the PDC photons but also allows to highlight a remarkable link between the discrete and continuous variable descriptions of PDC. We numerically analyze PDC processes with different conditions to demonstrate the versatility of our approach, which is applicable to a large number of current PDC sources.