Polarization and frequency disentanglement of photons via stochastic polarization mode dispersion

TL;DR

This paper studies how polarization and frequency of photons decohere during fiber transmission, revealing that entanglement can be destroyed or preserved depending on the state and fiber configuration.

Contribution

It introduces an analytical framework for understanding polarization and frequency decoherence in photons using a master equation approach.

Findings

Complete polarization disentanglement occurs at finite distance.

Frequency entanglement can survive at any finite distance for Gaussian states.

Decoherence behaviors differ for single-photon and two-photon states.

Abstract

We investigate the quantum decoherence of frequency and polarization variables of photons via polarization mode dispersion in optical fibers. By observing the analogy between the propagation equation of the field and the Schr\"odinger equation, we develop a master equation under Markovian approximation and analytically solve for the field density matrix. We identify distinct decay behaviors for the polarization and frequency variables for single-photon and two-photon states. For the single photon case, purity functions indicate that complete decoherence for each variable is possible only for infinite fiber length. For entangled two-photon states passing through separate fibers, entanglement associated with each variable can be completely destroyed after characteristic finite propagation distances. In particular, we show that frequency disentanglement is independent of the initial polarization status. For propagation of two photons in a common fiber, the evolution of a polarization singlet state is addressed. We show that while complete polarization disentanglement occurs at a finite propagation distance, frequency entanglement could survive at any finite distance for gaussian states.