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Photonics for Quantum (PfQ)

A detailed model for polarization mode dispersion in broadband polarization-encoded QKD

V.E. Rodimin, Konstantin Kravtsov, Rui Ming Chua, Gianluca De Santis, Alexei Ponasenko, Yury Kurochkin, Alexander Ling, James A. Grieve

Published Aug 2, 2024• 0 citations
Publisher

Abstract

We study Polarization Mode Dispersion (PMD) in fiber-based Quantum Key Distribution (QKD) using a broadspectrum polarization-entangled photon source. We analyze wavelength-dependent polarization transformations over 10 km deployed fiber channels, with measurements spanning one year of evolution. By examining the rotation of polarization states on the Poincare sphere and projecting them along a PMD trajectory onto a predefined state within a measurement basis, we derived a simple new formula that accurately links the measurement error probability to finite signal bandwidth and the observed differential group delay (DGD). Finally, we propose strategies to mitigate the PMD effect for entangled-based QKD by optimizing the orientation of the measurement bases and by performing the optimal spectral filtering of the source.

DOI
10.1117/12.3026922

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We study Polarization Mode Dispersion (PMD) in fiber-based Quantum Key Distribution (QKD) using a broadspectrum polarization-entangled photon source. We analyze wavelength-dependent polarization transformations over 10 km deployed fiber channels, with measurements spanning one year of evolution. By examining the rotation of polarization states on the Poincare sphere and projecting them along a PMD trajectory onto a predefined state within a measurement basis, we derived a simple new formula that accurately links the measurement error probability to finite signal bandwidth and the observed differential group delay (DGD). Finally, we propose strategies to mitigate the PMD effect for entangled-based QKD by optimizing the orientation of the measurement bases and by performing the optimal spectral filtering of the source.
We present a method for characterizing depolarization in fiber channels carrying broadband polarization-encoded optical signals. Wavelength-dependent polarization mode dispersion maps each input polarization to a trajectory on the Poincaré sphere; we show that the singular value decomposition of the band-averaged rotation matrix yields, in closed form, the optimal input states, the associated mutually unbiased measurement bases, and the resulting projection error probabilities. The three singular values provide a compact, bandwidth-dependent channel signature that distinguishes first- from higher-order dispersion, and yield the bandwidth at which the worst-case error probability reaches 3% as a practical filtering budget. We perform a second-order analysis of the band average that treats the two higher-order mechanisms: variation of the differential group delay at a fixed principal-state axis and wander of that axis with wavelength. We characterize 12 deployed fiber links in Masdar City and demonstrate mitigation by concatenating two channels through a single polarization controller, a step towards nonlocal compensation. The analysis is implemented in an openly available Python library for fiber-channel characterization.
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.
Quantum key distribution (QKD) is on the brink of being deployed on a large scale. For a successful launch it is important though, that QKD devices can be incorporated into or use existing telecom networks. Although not at telecom wavelengths, QKD based on polarization entanglement has already been shown over 1.4 km outside the laboratory. However, it was thought that dispersion effects, mainly polarization mode dispersion (PMD), in optical fibers will limit the use of polarization entanglement for longer distances. We report the distribution of quantum correlations over a record length of 100 km in telecom fibers with such a high quality that it would be possible to extract a secret key without background subtraction.
The performance of Quantum Key Distribution (QKD) protocols that encodeinformation in the polarization state of light can be affected by polarizationtransformations induced by the optical fiber channel. This thesis investigates whethera real, deployed fiber link can support polarization-based QKD, building on apolarization stabilization system developed in an earlier project course to activelycorrect the fiber’s polarization drift. To answer this, the channel-induced quantum biterror rate (QBER) is decomposed into a rotation-induced misalignment term,correctable by active polarization stabilization, and a depolarization term set by thefiber’s differential group delay (DGD) relative to the coherence time of thetransmitted photons, a term no stabilization system can correct. The stabilizationsystem’s performance and the fiber’s Polarization Mode Dispersion (PMD) vector,from which the DGD is extracted via a wavelength-swept Jones matrix reconstructionmethod, are both characterized experimentally on two deployed metropolitan fiberlinks in the Stockholm area. The results show the rotation term is fully within reachof the stabilization system, and reduce the remaining question — whether thedepolarization term is also acceptable — to a single, precisely defined externalparameter, the coherence time of the photon source eventually used for the quantumsignal, which this thesis shows exactly how to evaluate.
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.
We characterize theoretically and experimentally the degradation of polarization entanglement in a fiber-optic entanglement distribution system where one of the optical fibers is exposed to the effects of polarization mode dispersion (PMD). We show gradual reduction of entanglement with increasing PMD and find that the highest PMD tolerance is achieved when the bandwidth of the pump used to generate the entangled photons in a χ((3)) process is approximately half the bandwidth of the quantum channels.