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International Conference on Telecommunications

Analysis of polarization mode dispersion effect on quantum state decoherence in fiber-based optical quantum communication

Shamsolah Salemian, Shahram Mohammadnejad

Published Jan 1, 2011• 1 citation

Abstract

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.

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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 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 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.

The polarization mode dispersion (PMD) in optical fibers poses a major challenge for maintaining the fidelity of quantum states for quantum communications. In this work, a comprehensive model linking the probability of quantum measurement errors (infidelity) to PMD is developed and validated by experimental measurements of differential group delay and quantum bit error rate (QBER). Our research proposes effective methods to mitigate PMD effects for broadband entangled photons and evaluates the impact of higher-order PMD effects. The model provides an experimentally verified framework for the optimization of commercial quantum key distribution systems in deployed fiber-optic lines.

We investigate the polarization state dynamics of single photon pulse for optical fiber quantum communication channels. On the basis of a birefringence vector model in which amplitude and direction are both stochastic variables, Jones vector is obtained by solving the frequency domain wave equation. The fidelity of output quantum state and degree of polarization of the pulse are also obtained from the density operators. It is shown that the fidelity of quantum state decreases quickly and tends to a stable value along optical fiber, and increases for larger mean fluctuation magnitude of the stochastic fiber birefringence. Degree of polarization is nearly constant for small mean fluctuation magnitude of the birefringence. The fidelity and degree of polarization vary in the same way for Gaussian and rectangular frequency spectrum envelope, while the value of Lorentzian spectrum is smaller.

Affected by PMD(Polarization Mode Dispersion),the polarization state of the single photon will be randomly and slowly altered during the transmission in the fiber.This increases the error probability at the receiving end.So a means for measuring the variance to the preprocess polarization state is required for the distribution of the quantum key.A sensor with balanced detection is introduced to the BB84 protocol and the theoretical model of the QBER(Quantum Bit Error Rate) is established with POVM(Positive Operator Valued Measurement).The variance of the polarization state is measured with the Wollaston prism and the error is eliminated for the dual channel.The angle tolerance of the Wollaston prism is 0.1° and the numerical analysis by the use of the QBER model shows the new protocol decreases the error rate to 3.05×10-6.