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AIP Advances

Stochastic decoherence induced by polarization mode dispersion

Yiwen Liu

Published Jan 1, 2023• 2 citations
Publisher

Abstract

We address the propagation of entanglement in fibers and investigate the decoherence of polarization-entangled photon pairs caused by polarization mode dispersion (PMD). We devise a decoherence model starting from the statistical properties of polarization mode dispersion and obtain the density matrix describing initially maximally entangled states at any time. Using these results, we derive how decoherence depends on the length of the fibers. We calculate the mean concurrence of the entangled states with PMD effects as a function of fiber length, bandwidth, and other parameters in different cases.

DOI
10.1063/5.0101180

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We address the propagation of entanglement in fibers and investigate the decoherence of polarization-entangled photon pairs caused by polarization mode dispersion (PMD). We devise a decoherence model starting from the statistical properties of polarization mode dispersion and obtain the density matrix describing initially maximally entangled states at any time. Using these results, we derive how decoherence depends on the length of the fibers. We calculate the mean concurrence of the entangled states with PMD effects as a function of fiber length, bandwidth, and other parameters in different cases.
We investigate the effects of polarization mode dispersion (PMD) on the propagation of single- and two-photon states in single-mode fibers. We look at PMD as decoherence due to the system's coupling with the bosonic environment involved in optical birefringence and a thermal bath, respectively. The evolution of the polarization density matrix is described by a master equation, and its solution is used to calculate the differential group delay (DGD) due to the fiber. The PMD effects on the dynamics of EPR states in optical fibers are investigated by using the same method. In both the short-time and long-time regimes, we find that PMD-induced and thermal-induced decoherence behave similarly.
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.
The implementation of quantum communication protocols in long optical fibers is limited by several decoherence mechanisms. In this contribution we review this mechanisms and analysis their effect on the quantum states. Because of asymmetry in the real fibers, the two orthogonal polarization modes are propagated at different phase and group velocities. The difference in group velocities results in Polarization Mode Dispersion (PMD). It is created by random fluctuations of the residual birefringence in optical fibers, such that the State of Polarization (SOP) of an optical signal will turn randomly over time, in an unpredictable way. In optical quantum communication, quantum state measurement is necessary. The bottleneck for communication between far apart nodes is the increasing of the error probability with the length of the channel connecting the nodes. For an optical fiber, the value of absorption and depolarization of a photon (i.e., the qubit) increases exponentially with the length of the fiber.
We present a study of nonlocal polarization-mode dispersion (PMD) compensation in the framework of quantum information theory. We consider distribution of polarization-entangled photon pairs through optical fibers, where PMD acts as a decoherence mechanism. The use of additional controlled PMD in one of the two optical paths can restore the original degree of entanglement fully or in part, depending on the system configuration, in a nonlocal fashion. Using the quantum analog of the Shannon entropy, the Von Neumann entropy, we evaluate the quantum mutual information of propagated polarization-entangled photon pairs as a function of the fiber-channel PMD, and quantify the beneficial effect of nonlocal PMD compensation in terms of mutual quantum information restoration. All the relevant quantities can be extracted from the reduced density matrix characterizing the twophoton state polarization, which is obtained experimentally by means of customary polarization tomography.