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An information-theoretical treatment of nonlocal PMD compensation

Gabriele Riccardi, Brian T. Kirby, Cristian Antonelli, Michael Brodsky

Published Feb 28, 2020• 4 citations

Abstract

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.

DOI: 10.1117/12.2546523

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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.

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.

Entanglement distribution through optical fibers is essential for quantum communication networks; however, fiber transmission can alter photon polarization and modify the observed correlations of polarization-entangled states, necessitating polarization compensation to recover the desired entangled state in the measurement basis. Here, we experimentally evaluate two passive polarization compensation techniques: a free-space Quarter-Half-Quarter (QHQ) waveplate configuration and an in-fiber three-paddle Fiber Polarization Controller (FPC). The polarization transformation along each downconverted-photon path is independently compensated through a systematic path-by-path optimization procedure. Using both techniques, we recover high-quality polarization correlations and entanglement, with visibilities exceeding

93\%

in three mutually unbiased bases and fidelities above

94.5\%

. The results demonstrate comparable restoration using free-space waveplate-based and fiber-based control, establishing a systematic framework for laboratory and short-reach quantum communication links.

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.