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Opto-Electronics Review

Testing of a four-channel Stokes polarimeter performance for intrusion detection in QKD systems

Estera Pawlikowska, Marek Życzkowski, Anna Pakuła, Paweł Marć

Published Dec 17, 2024• 0 citations
Publisher

Abstract

The most mature quantum key distribution systems available on the market is the class of prepare-and-measure systems which are vulnerable to eavesdropping attacks. Therefore, monitoring optical properties of such a system should be enhanced. This paper presents a measurement methodology, characterisation, and testing of a four-channel Stokes polarimeter implemented into the send-and-return quantum key distribution system with faint pulses. The developed polarimetric setup is a complete amplitude-division Stokes polarimeter, the main objective of which is to define changes in the polarization state of light pulses. The measurement method is based on intensity measurements of four selected polarization components. The four-channel Stokes polarimeter was characterised and its performance was compared with a commercial instrument. At this stage of the polarimeter development, different signal processing paths were proposed. The influence of fibre infringement was observed as a rapidly changing polarisation state and, as a result, intrusion threshold levels were determined for the analysed signals for the quantum key distribution fibre-optic link tested.

DOI
10.24425/opelre.2025.153182

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The most mature quantum key distribution systems available on the market is the class of prepare-and-measure systems which are vulnerable to eavesdropping attacks. Therefore, monitoring optical properties of such a system should be enhanced. This paper presents a measurement methodology, characterisation, and testing of a four-channel Stokes polarimeter implemented into the send-and-return quantum key distribution system with faint pulses. The developed polarimetric setup is a complete amplitude-division Stokes polarimeter, the main objective of which is to define changes in the polarization state of light pulses. The measurement method is based on intensity measurements of four selected polarization components. The four-channel Stokes polarimeter was characterised and its performance was compared with a commercial instrument. At this stage of the polarimeter development, different signal processing paths were proposed. The influence of fibre infringement was observed as a rapidly changing polarisation state and, as a result, intrusion threshold levels were determined for the analysed signals for the quantum key distribution fibre-optic link tested.
We present the results of simplified polarimetric methods for detecting disturbances on a fibre-optic link in a quantum key distribution system. The proposed methods use a polarisation coupler and a single polariser as a polarisation-sensitive detection system. The effectiveness of the disturbance detection was considered in a plug-and-play quantum key distribution system with phase encoding. This paper compares the performance of two simplified methods for determining changes in the state of polarisation in response to three types of disturbances, including touching, bending, and inserting a clip-on coupler. Also, the results of an experiment involving the entire procedure of introducing eavesdropping into a telecommunications fibre-optic cable are presented. The results of the measurements indicate the subsequent steps when attacking a fibre-optic cable. This article shows that a simplified polarisation-sensitive sensor can be implemented into a quantum key distribution system to detect disturbances and eavesdropping attempts, as well as enhance the security of the system.
Quantum Key Distribution (QKD) employs the laws of quantum mechanics for the purpose of cryptography. Two parties, commonly called Alice and Bob, are able to share a random key which is used to encrypt a message. Any eavesdropper trying to intercept their key will have to make measurements, thereby disturbing the system. This can be detected by Alice and Bob and they will then discard their key. Polarisation encoded QKD protocols use the polarisation of single photons as qubits to generate a cryptographic key. This can be implemented using a fibre optic link between Alice and Bob but the polarisation of light is altered when passed through a fibre due to birefringence caused by asymmetries in the fibre. This causes refractive differences for orthogonal components of the state of polarisation of light, so the polarisation is rotated as the photon is transmitted through the fibre. If the fibre is fixed, the change of polarisation will be unique and constant. This can be compensated by rotating each photon appropriately to its original state. Under typical environmental conditions, such as temperature changes and vibrations, the birefringence effects vary and should be compensated in real time. Therefore, an active polarisation controller is needed in order to maintain the state of polarisation of each qubit. An investigation was done to first track how the state of polarisation changes over time in a natural environment. Both wavelength-division multiplexing and time-division multiplexing were investigated as testing methods for the compensation system. A timedivision multiplexed system was developed to compensate the changes in polarisation. Since QKD protocols such as BB84 and B92 utilise two non-orthogonal bases, two polarisation controllers are usually used for compensation. However, by using a search algorithm, one polarisation controller was able to isolate the plane on the Poincare sphere that passes through both bases, thus compensating non-orthogonal states with one device.
Quantum key distribution (QKD) enables remote users to establish secret keys secured by quantum mechanics. Polarisation encoding offers simple state preparation and measurement; however, fibre birefringence, component imperfections, and high-speed polarisation modulation make stable, low-error operation challenging. This thesis investigates the development of a high-speed polarisation-based QKD transmitter. The optical components, including intensity and phase modulators, interferometric systems, and electronic polarisation controllers (EPCs), are characterised experimentally. Gradient descent, coordinate gradient descent, and simulated annealing are compared for EPC-based state preparation. With a 50 mV step, coordinate gradient descent is approximately six times faster than conventional gradient descent, while simulated annealing achieves 100% success over the tested runs at the selected settings. The polarisation-control approach is evaluated in a proof-of-concept BB84 feasibility experiment over a deployed 224 km undersea fibre link between the United Kingdom and Ireland, with a measured attenuation of 38.6 dB. Channel loss and polarisation stability are characterised, and the QBER is measured using SPAD and SNSPD detector configurations. At a mean photon number of one, the SNSPD configuration produces average QBERs of 2.98% and 1.55% for the horizontal and vertical states, respectively, substantially below the corresponding SPAD results. Separately, a field-trial-informed asymptotic decoy-state model projects a maximum secret-key yield of 2.93*10^-6 bit/clock. Finally, several iterations of high-speed polarisation-encoders are developed and assessed, identifying extraction efficiency and fibre-axis alignment as key practical constraints. The resulting hybrid encoder prepares four polarisation states at 40 MHz, with measured overall system QBERs below 3%. Overall, the work establishes practical methods for polarisation control, long-distance feasibility assessment, and stable high-speed state preparation in polarisation-based QKD systems.
This thesis presents experimental realizations of quantum key distribution (QKD) systems which are based on continuous variables. As such, polarization or amplitude and phase of a light field are used, in contrast to discrete variables like the photon number. One QKD-system examined in this work is based on the entanglement of intense light pulses in the amplitude and phase quadratures. A measurement system for these observables is built and characterized. The existing measurement procedures can be optimized in speed, such that a observation of entanglement at a rate of 100 kHz is possible. Future improvements of the measurement system to obtain a secure key generation are presented. The second group of experimentally investigated QKD-setups uses classical coherent states and homodyne detection. An absolute correspondence between the quantum mechanical description of the system and the state preparation and measurement apparatus is given. It is shown that quadrature variables can be substituted with polarization variables, providing significant technical advantages. A setup to generate arbitrary continuous variable polarization states is built and characterized, as well as a low noise, broadband and high efficiency homodyne polarization detection system. Its overall efficiency, including optical and photodiode loss, and interference visibility is up to 88%. Using these setups, different coding schemes for quantum key generation were implemented. Transmissions with pulse rates of 100 kHz and quantum channel losses up to 74% (-5.9 dB respectively) were experimentally simulated. By using the post selection method, correlated key pairs secure against beam splitting attacks could be obtained. A special detection setup, using simultaneous measurement of conjugate polarization observables, provides tomographical data (e.g. the Q-function) of the transmitted states. Thus, an advanced security analysis against more general attacks will be possible.
Due to the fast-paced advancements of the quantum computing field, current public key cryptographic protocols need to be rethought. One promising solution is Quantum Key Distribution (QKD), whose security is robust to any computational advancement. The security of QKD relies on the laws of quantum mechanics, ensuring that any eavesdropper attempting to access the data will be detected. In particular, polarization-encoding QKD systems allow to generate secret keys in two remote locations to encode/decode information, using the State of Polarization (SOP) of single photons. Although its security has been theoretically proven, its practical implementation poses some challenges, part of which are the main focus of this PhD thesis. One relevant process in QKD systems is the synchronization between the transmitter and receiver, namely, the frame synchronization. This way, in this thesis, a frame synchronization method is developed and implemented, showing its potential for the use in prepare-and-measure QKD systems. The developed method has been shown to be effective, even with a low number of photons reaching the receiver. Furthermore, its architecture allows it to be adjusted for different attenuation regimes of the QKD system. The ability to encode data on the physical properties of single photons, in this case, polarization, highly depends on the capacity to accurately generate the required polarization states on demand. This way, an automatic SOP generation method, comprising an optical polarization monitoring system and a dedicated algorithm was developed and implemented, capable of generating four SOPs. This method reached an average Quantum Bit Error Rate (QBER) of 0.75%, which is well below the security threshold. After the SOP generation, and their transmission through the quantum channel, polarization alignment algorithms are required to compensate for the random rotations induced by birefringence in the optical fiber. In this thesis, a non-iterative polarization compensation method was implemented. This method requires only three QBER estimations to re-align the polarization, reaching average QBERs of 1.8%. Additionally, multiple iterative methods were implemented for comparison purposes, with the results clearly showing a better efficiency of the deterministic method. Beyond fiber-based transmissions, free-space transmissions were analysed due to their ability to reach sites without installed fiber and due to its potential for satellite-based quantum communications. This thesis demonstrates the feasibility of polarization-encoding QKD over free-space channels, by subjecting quantum signals to atmospheric turbulence to study its impact. In that sense, polarization variations over a 1.8 km outdoor free-space channel were monitored, to understand the effect of atmospheric turbulence on polarization. These results have shown that SOP variations in free-space links are slow, allowing their compensation. Furthermore, it was identified that, under conditions tested, the Secret Key Rate (SKR) could reach values up to 8.7×10ˉ⁴ bits per second, allowing QKD over free space for distances up to 2.31 km.